Sparse canopy parameterizations for meteorological models B.J.J.M. van den Hurk
Sparse canopy
parameterizations for
meteorological models
B.J.J.M. van den Hurk
Promotor Dr. J. Wieringa, hoogleraar in de meteorologie
Co-promotor Dr. H.A.R. de Bruin, universitair hoofddocent meteorologie
Sparse canopy
parameterizations for
meteorological models
BJ.J.M. van den Hurk
Proefschrift ter verkrijging van de graad van doctor in de landbouw- en milieuwetenschappen op gezag van de rector magnificus dr C.M. Karssen in het openbaar te verdedigen op maandag 22 januari 1996 des namiddags te vier uur in de Aula van de Landbouwuniversiteit Wageningen
ÖTOM^
CiP-gegevens Koninklijke Bibliotheek, Den Haag
Hurk, B.J.J.M. van den
Sparse canopy parameterizations for meteorological models/ B.J.J.M. van den Hurk. - [S.l. : s.n.]. - m Thesis Landbouwuniversiteit Wageningen. - With réf. - With summary in Dutch. ISBN 90-5485-491-X Subject headings: SVAT-schemes / sparse canopies / landsurface-PBL interactions.
NWO Coverpage Christien van den Hurk-Alferink What's UNDER the surface?
Financial support This study was carried out at the Department of Meteorology of the Wageningen Agricultural University. Financial support was provided by the European Committee under contract number EPOC CT90 - 0030, and by the Netherlands Organisation for Scientific Research (NWO) under contract number 762-365-030.
Abstract
Meteorological models for numerical weather prediction or climate simulation require a description of land surface exchange processes. The degree of complexity of these land-surface parameterization schemes — or SVAT's — that is necessary for accurate model predictions, is yet unclear. Also, the calibration of these SVAT's for relatively complex terrain, such as sparse canopies, is not completely resolved. This thesis pays attention to the sensitivity of the atmospheric boundary layer to the parameterization of surface exchange processes for a sparse canopy surface.
During two experimental campaigns carried out in a sparsely vegetated vineyard surface in La Mancha, Spain, detailed measurements were collected, including the flux densities of sensible, soil and latent heat, radiative fluxes, aerodynamic properties, and soil and vegetation characteristics. These measurements were used for calibration and validation of various SVAT-models and their components.
In a theoretical analysis the traditional treatment of aerodynamic transport of heat and moisture between a sparse canopy surface and the atmosphere was considered, and compared by an alternative formulation based on Lagrangian diffusion theory. An analysis of field observations was carried out to quantify the spatial and temporal variability of the surface albedo of a sparsely vegetated surface. Furthermore, a model for the stomatal conductance, based on the calculation of leaf photosynthesis and its relations with stomatal water vapour transport, was tested and scaled-up to the canopy level.
Various existing SVAT's, designed for sparse canopies, were described and compared to field measurements in a zero-dimensional mode, that is, with forcings measured at reference height close above the surface. These models were all based on different physical treatment of soil heat flux, aerodynamic exchange and canopy resistance. None of the included models gave an optimum description of the observed fluxes, but a model could be constructed that combined the best parts of each of these SVAT's.
In an additional model study, this new description has been coupled to a one-dimensional planetary boundary-layer (PBL) model. Parts of the SVAT were replaced by other components, and the impact on simulated PBL-dynamics has been evaluated. Large effects are found when (a) the reference two-layer model was replaced with a single layer ('big leaf') model, (b) soil heat flux was simulated with a resistance scheme rather than a diffusion or force-restore scheme, and (c) the aerodynamic resistance between the reference level and the bare soil was chosen too low. Since vegetation cover was small, smaller effects resulted from an alteration of the canopy resistance formulation. Also, it was found that the simulated entrainment of heat at the top of the boundary layer is low compared to entrainment ratios cited in literature.
Keywords: sparse canopy, surface fluxes, surface-PBL interaction, land-surface processes.
Dit boek draag ik op aan mijn vader en mijn moeder
Voorwoord
Het eeuwige dilemma tussen 'het perfecte levenswerk' en 'het is maar een proefschrift' is op het werk dat in dit boek beschreven staat zeker van toepassing. Het onderwerp: modellering van land-oppervlak processen in meteorologische weer- en klimaatmodellen. Het materiaal waar uit te putten is: een erg groot aantal bestaande land-oppervlakmodellen, met ieder een eigen gedachtengang, behoefte aan invoergegevens, en mate van beschikbare documentatie en validaties. De opdracht: een vooral 'eerlijke' vergelijking tussen een aantal van die modellen uit te voeren met behulp van een zelf verzamelde dataset. Het lijkt een overzichtelijke opgave, maar de waarheid is anders.
Nog helemaal niet van plan om te promoveren kreeg ik na mijn vervangende diensttijd aan de vakgroep Meteorologie een aanstelling als EFEDA-projectmedewerker (wordt in dit boekje verder uitgelegd). Een jaar daarvoor begon Anno van Dijken in het kader van een promotie-baan moedig aan het uitvissen van de benodigde mate van detail in land-oppervlakmodellen voor meteorologische toepassingen, en wisselde deze onderzoeksopdracht in voor een baan bij MeteoConsult. Hij liet een portie denk- en programmeerwerk achter waar ik dankbaar gebruik heb kunnen maken. Want, van Henk de Bruin kreeg ik het verzoek het promotie-onderzoek af te ronden. Na wat aarzelen, en wat passen en meten met betrekking tot een kleine bijstelling van de oorspronkelijke onderzoeksvraag — zodat ik het werk wat ik voor EFEDA had gedaan grotendeels kon gebruiken voor het proefschrift — heb ik deze baan aanvaard. Aan deze Henk de Bruin dank ik niet alleen een slordige zes jaar betaald werk, maar bovendien een enorme bijdrage in de vorm van morele steun, kritische en vaak zeer praktisch georiënteerde vragen, contact met een flink aantal vakmensen binnen en buiten de EFEDA-gemeenschap, een gezonde dosis twijfels en een even grote dosis zelfvertrouwen, een muziek-compagnon op diverse feestjes, een gewillig oor voor boze en vreugdevolle momenten, en zo kan ik nog wel even doorgaan. Hij is verder een drijvende kracht achter gigantisch veel werk op de vakgroep, en mijn dank voor al deze bemoeienis is groot, bijzonder groot.
Ik weet eerlijk gezegd niet of ik collega-promovendi zoals met name Anne Verhoef, Cor Jacobs, Berenice Michels, Rushdi El-Kilani, Aafke Atzema, Joost Nieveen, Job Verkaik en Theo Jetten nou moet bedanken, of dat ik gewoon maar blij moet zijn met hun aanwezigheid en onze wederzijdse contacten. Nou ja, Anne is natuurlijk een maat uit duizenden geweest. Samen zweten in Spanje tijdens de EFEDA-campagne, de talloze gesprekken en small-talks over alles in onze werkkamer en daar buiten, en ook het sterke gevoel van solidariteit die gepaard ging met de gezamenlijke eindsprint voor een proefschrift in het laatste jaar. Als dankjewel het goede woord hiervoor is, nou, dan dankjewel. Aan Cor ben ik een vergelijkbare dosis solidariteit verschuldigd, maar omdat hij nou eenmaal anderhalf jaar voor liep op ons functioneerde hij ook als veelgebruikte vraagbaak en brainstorm-tank. Ook dankjewel. Kamer- en EFEDA-genoot Berenice, de talloze bieren bij José van Alhambra (ook in Spanje) zijn memorabel, en daardoor blijvend. En we hebben samen een mooie poster gemaakt voor de vakgroep.
Collega-vakgroepsmensen zijn al net zo bedankbaar. Jon Wieringa, die tijdens mijn promotie-tijd als hoogleraar aantrad, en mij als een soort erfenis op zijn bord kreeg: bedankt voor de geleverde ondersteuning. Over ondersteuning gesproken: Bert Heusinkveld, het 'veulen' van EFEDA, een ware aanwinst voor de vakgroep: heel erg
dankjewel. Minstens zoveel dank verdienen Kees van den Dries, de computer-beheerder, Ad van den Berg en Rolf Krikke, programmeer-nymphen en kroegtijgers, Anton Janson, de levensgenieter van de werkplaats, en zijn Siamese tweeling Teun Jansen — de conversaties op 13m hoogte boven een Spaanse wijngaard zijn onvergetelijk. Frits Antonysen en Johan Birnie die een nieuwe ervaring aan hun levens toevoegden door het EFEDA-gebeuren, medezaalvoetballer Willy Hillen, en natuurlijk Dick Weigraven, met zijn eeuwig optimisme en bereidheid tot medewerking. Een gigantische ondersteuning kreeg ik ook van secretaresse Gerrie van den Brink en haar collega's (Annelies, Jolanda), voor de vele even-tussendoor-vraagjes-en-formuliertjes. Voor hen allen gold dat zij hun baan op een voor mij erg plezierige manier invulden. Heel veel bedankt daarvoor.
Van de stafmedewerkers Adrie Jacobs, Leo Kroon en Michael Saraber ontving ik naast een prettige hoeveelheid collegialiteit ook vaak repliek op mijn (semi-)wetenschap-pelijke beschouwingen. En Adries bijdrage aan het EFEDA-werk valt niet op de achterkant van een bierviltje te vermelden, en een extra dankjewel is bier op zijn plaats. Dit geldt overigens evenzeer voor de verschillende studenten die meer of minder tijd aan EFEDA hebben besteed en nog niet zijn genoemd: Arnold Moene, Erik Beek, Laurens Ganzeveld, Ad Jeuken, Harold ten Dam, en Diedert Spijkerboer.
This work is fun! It is funny to share lots of beers in Tomelloso with Henrik Segaard and his colleagues, and to share the enthousiasm about well-working material with Jan Eibers, Han Dolman and other members of the Winand Staring Centre. It has also been a pleasure to have worked with the people from the French Meteorological Service CNRM, in particular with Pierre Bessemoulin and Joel Noilhan. Joel probably helped me a lot to convince me that the EFEDA-work should be converted into a PhD-thesis. And now he helps me even more by playing the role of criticizer in my promotion committee. I am grateful to that, as I am grateful to Bert Holtslag, Hans Vugts and Reinder Feddes. The EFEDA-community consists of many more people with whom I have experienced a pleasant collaboration, and taking the risk for forgetting people for granted, I would like to thank the people from the Amsterdam Free University, Yadvinder Malhi, Ford Cropley and others from the Reading University, the Wageningen colleagues Rene Kim, Wim Bastiaanssen, Peter Droogers, Han Strieker and a lot more, Martina Berger and others from the Free University of Berlin, Kevin Sene, Howard Oliver, Colin Lloyd, Eleanor Blyth and colleagues from the Institute of Hydrology in Wallingford, and Antonio Brasa and others from the University of Albacete.
Apart from this long list of colleague scientists, I am particularly greatful to the inspiration I have pleasantly received from a few great (micro)meterologists: Keith McNaughton from HortResearch, Palmerston-North, New Zealand, who has spent an awfully large amount of time and patience in explaining how Lagrangian theory should be interpreted, how to write that down in a scientific paper, how moths can be used as meteorological sensor, how Christmas looks in summer, and, last but not least, how people are dressed for weddings in New Zealand. His participation to my wedding in April 1994 was a party on its own, and he once more proved himself to be a very pleasant and easy-to-go-along-with person. In an earlier stage, Dennis Baldocchi brought me irreversably on the path of scientific research, by sharing his great enthousiasm while I visited Oak Ridge. John Monteith, who has effectively "invented" many ideas micro-meteorologists work with nowadays, sincerely inspired me at a few occasions, in particular during the evaporation workshop in Copenhagen. And finally, the many conversations with Anton Beljaars about now-adays SVAT's (see this booklet) turned out to be productive enough for writing a joint scientific paper. And of course, I thank him a lot for showing his confidence in me by offering a job at KNMI.
Mijn hart gaat naar veel dingen. Natuurlijk naar mijn vrouw Christien, die me met zoveel dingen heeft geholpen. Maar ook naar 'mijn' theatergroep De Stichting Lens, waar ik een hele berg van de inspiratie die nog over was naast mijn werken aan SVAT's kwijt kon. Een groep bestaat uit mensen, en de mensen van Lens worden erg bedankt.
Contents
Abstract 5
Voorwoord 6
1. Introduction 11 1.1 Atmosphere - land surface interaction 11 1.2 Land surfaces and land-surface models 14 1.3 A sensitivity analysis using a coupled SVAT-PBL model 15 1.4 Organization of the thesis 18
2. Data collection and processing 20 2.1 The EFEDA-experiments 20
2.1.1 Context and goal 20 2.1.2 EFEDA-I 21 2.1.3 EFEDA-II 22 2.1.4 Correspondence of goals 23
2.2 Measurements taken by WAUMET during EFEDA-I (1991) 23 2.2.1 Site description 23 2.2.2 General set-up of WAUMET 24 2.2.3 Determination of available radiative energy 28 2.2.4 Determination of scalar and momentum flux densities 30 2.2.5 Determination of soil heat flux density 38 2.2.6 Determination of vegetation parameters 40 2.2.7 Various determinations 46
2.3 Measurements taken by WAUMET during EFEDA-II (1994) 47 2.3.1 General setup 47 2.3.2 Site description 49 2.3.3 Determination of available energy and surface temperature 50 2.3.4 Determination of scalar and momentum flux densities 51 2.3.5 Soil measurements 52 2.3.6 Determination of vegetation parameters 53
2.4 Derived quantities 57 2.4.1 Aerodynamic roughness and displacement height 57 2.4.2 Roughness length for heat 59 2.4.3 Energy balance terms 61 2.4.4 Soil thermal properties 65
3. Aerodynamic transfer, albedo, and crop conductance for a sparse canopy surface 68 3.1 Introduction 68 3.2 Aerodynamic transfer 69
3.2.1 Concepts based on diffusion theory 69 3.2.2 Implementation of near-field dispersion in a simple two-layer
surface resistance model 70 3.2.3 A 'Lagrangian' revision of the resistors in the two-layer
model for calculating the energy budget of a plant canopy 80
• 8 Sparse canopy parameterizations for meteorological models
3.3 The albedo of a sparse vineyard canopy during the growing season 87 3.3.1 Processes determining the albedo of a sparse vineyard
canopy 88 3.3.2 Albedo measurements taken in a sparse vineyard canopy 92 3.3.3 Conclusions 97
3.4 A photosynthesis model for the crop conductance applied to a sparse vineyard canopy 98 3.4.1 Theory 99 3.4.2 Site description and measurements 101 3.4.3 Results 102 3.4.4 Discussion and conclusions 103
3.5 Conclusions 106
4. Selected surface layer and boundary layer models 108 4.1 Surface layer models for sparse canopies 108
4.1.1 The modified big-leaf model 109 4.1.2 The ECMWF surface scheme 111 4.1.3 Impact of some simplifying assumptions in the new ECMWF-
surface scheme 116 4.1.4 The two-layer model of Deardorff 129 4.1.5 The two-layer models of Shuttleworth & Wallace and
Choudhury & Monteith 136 4.2 Treatment of the planetary boundary layer 142
4.2.1 A numerical diffusion scheme for the planetary boundary layer 142
4.2.2 Slab model for the convective PBL 144 4.3 Limitations to the coupled 1-dimensional atmospheric model 146
5. An intercomparison of three soil/vegetation models for a sparse vineyard canopy 148 5.1 Description of data, model settings and used forcings 150
5.1.1 Collected data 150 5.1.2 Forcings and specific model settings 151
5.2 Simulations with the SVAT-schemes 155 5.2.1 Soil heat flux density 156 5.2.2 Sensible heat exchange and surface temperature 158 5.2.3 Evaporation and soil water budget 160
5.3 Discussion and conclusions 162
6. Sensitivity of the planetary boundary layer to surface description 165 6.1 Model specification 167
6.1.1 The reference model 167 6.1.2 Model variations 168
6.2 Set-up of the sensitivity analysis 172 6.2.1 Basic strategy 172 6.2.2 Specification of considered SL- and PBL-parameters 174 6.2.3 Radiative forcings and initial profiles 175
6.3 Results of the sensitivity analysis for daytime conditions 177 6.3.1 The surface representation group 178 6.3.2 The soil heat and water vapour flux group 182 6.3.3 The aerodynamic exchange group 186 6.3.4 The canopy resistance group 188 6.3.5 PBL-sensitivity and an analytical approach 191
Contents
6.4 Results of the sensitivity analysis for nighttime conditions 194 6.4.1 The surface representation group 194 6.4.2 The soil heat and water vapour flux group 195 6.4.3 The aerodynamic exchange group 196 6.4.4 The canopy resistance group 197
6.5 Simulations using EFEDA-observations 197 6.5.1 Selection of the simulation period 198 6.5.2 Initialization and forcing 199 6.5.3 Control run 200 6.5.4 Results of the sensitivity analysis 202
6.6 Discussion and conclusions 207 6.6.1 Differences of model parts 208 6.6.2 Practical considerations for SVAT's 212 6.6.3 Guidance for future research 213
Appendix I: List of symbols and acronymns 215
Appendix II: Instrumental aspects and data processing 220 1 Low-pass filtering (detrending) 220 2 Eddy-correlation corrections 221 3 Surface temperature and radiometer corrections 232 4 Soil heat flux density corrections 235
Appendix III: The bulk leaf boundary-layer resistance 236
Appendix IV: The photynthesis model at the leaf scale and calculation of
ambient conditions 238
Appendix V: Numerical aspects of the SVAT-models 241
Appendix VI: Values of the surface layer and boundary layer parameters,
calculated with the reference SVAT coupled to the PBL-model 245
Samenvatting 247
Summary 254
Literature 261
Curriculum 271
10 Sparse canopy parameterizations for meteorological models
1 The gap between politicians ana
climate researchers is difficult to bridge,
as long as politicians don't understand politics,
and climate researchers don't understand climate
Introduction
The population living on the Earth's surface is very familiar with processes as
heating of the air after sunrise, wilting of crop leaves after a long period without rain, or the
development of cumulus clouds by the end of a summer day. These processes are all simple
results of a complex set of interactions between the surface and the air just overlying the
ground. When the soil receives radiation, it returns this energy partially back into the
atmosphere by heating it, or by using this energy for evaporation, humidifying the air.
Heating the air above the ground enhances turbulence intensity, which can cause intense
mixing with higher air layers. In its turn, this affects the state of the air near the surface.
Rising of moist air can also result in the formation of clouds, which will modify the amount
of radiation penetrating to lower levels, or can eventually cause rain (Mcintosh and Thorn,
1983). The land surface and the overlying atmosphere clearly interact.
This thesis reports on a study of this interaction. It pays attention to the transport of
water vapour, sensible heat and momentum between the surface and the atmosphere. It
focusses on a surface that is only partially covered with vegetation. The framework is
provided by measurements, theoretical analysis, and modeling efforts. In this chapter we
will discuss the atmosphere-land surface interaction in more detail, and an outline and the
main purposes of the research will be given.
Atmosphere - land surface interaction
Generally, the land surface-atmosphere interaction influences the dynamics of the
entire atmosphere, both on the shortterm regional and the longterm global scale. The
transfer of momentum and sensible and latent heat between the surface and the atmosphere
primarily modifies the local surface and air adjacent to it, but atmospheric motions act as a
major redistributor of energy at a global scale (Schmugge and André, 1991).
By conducting experiments with atmospheric General Circulation Models, GCM's, it
2. Introduction 11 •
has been shown that the large end of the range of spatial and temporal scales, the global
climate, is sensitive to the land-surface exchange processes (Garratt, 1993). Early GCM studies
revealed a climate sensitivity to surface evaporation and initial soil moisture content, albedo,
or surface roughness (see reviews by Mintz, 1984, and Rowntree and Sangster, 1986). For
instance, Shukla and Mintz (1982) noticed a large reduction of continental precipitation over
most continents when a potentially evaporating surface was changed into a surface without
any evaporating at all using a GCM. Charney et al. (1977) found that an increase of the albedo
of the Sahelian region would lead to a reduction of both the regional evaporation and
precipitation in the area. Treatment of the transfer of water from deeper soil layers into the
atmosphere via transpiration plays a significant role in the long term predictions of cloud
development, precipitation, evaporation and soil moisture content (Milly and Dunne, 1994).
GCM studies were also applied to investigate the impact of large scale changes in vegetation
cover. Particularly, a series of simulations was dedicated to the effects of tropical
deforestation (Henderson-Sellers and Gornitz, 1984; Dickinson and Henderson-Sellers,
1988).
Also, at somewhat smaller timescales a sensitivity of atmospheric behaviour to land
surface description is evident. Beljaars et al. (1995) found a considerable difference in
predicted USA rainfall after changing the land surface parameterization scheme in the ECMWF
Numerical Weather Prediction (NWP) model. Moene et al. (1995) used the meso-scale High
Resolution Limited Area Model (HIRLAM) covering Western-Europe, and found very
different rainfall predictions for different soil moisture initializations.
At smaller time and spatial scales, the interaction with the Planetary Boundary Layer
(PBL) is important. The PBL is defined as the layer which is directly affected by the state of
the underlying surface. It senses the diurnal variations of the surface properties (such as the
surface temperature or evaporation) and adapts to a change of surface roughness. The
condition and growth of the PBL depends on the partition of available energy at the surface.
Using a numerical PBL-model with a simple energy balance scheme as lower boundary
condition, Troen and Mahrt (1986) found a non-linear reduction of the PBL height when the
surface evaporation was increased.
The turbulent mixing of air in the PBL partly determines the state of the atmosphere
at screen height, just above the surface. Since the driving force of heat and water vapour
exchange at the surface is the gradient of the particular constituent between the surface and
a reference level just above, feedback processes between the surface and the boundary layer
contribute to the properties of the lowest layers of the atmosphere (De Bruin, 1987). This
mechanism is denoted as PBL-feedback.
PBL-feedback can result in either an increase or a decrease of the effect of changing
surface properties on the energy balance of the surface. Jacobs and de Bruin (1992)
demonstrated that including PBL-dynamics implies a negative feedback on evaporation
when the crop resistance is modified: a reduction of the resistance causes at first instance an
increase of the evaporation, which results in a decrease of the humidity deficit at reference
height when boundary layer mixing is considered. Alternatively, positive feedback on
evaporation occurs when the net radiation is changed, for instance due to a changing
albedo. Both sensible and latent heat will be reduced when total radiant energy is reduced.
Accounting for boundary layer mixing, also a reduction of the reference temperature will be
• 12 Sparse canopy parameterizations for meteorological models
simulated, which reduces the humidity deficit and thus the evaporation. Rowntree (1991)
pointed at a positive feedback mechanism that occurs when the surface resistance increases
due to a removal of vegetation. A progressive reduction of the vegetation may be the result
of a drying atmosphere and a decrease of precipitation.
A second mechanism of feedback is the response of stomata to ambient conditions.
In coupled models in which the stomatal conductance for water vapour is reduced as the
ambient humidity deficit increases, a positive feedback on surface evaporation is simulated.
A reduction of evaporation will result in a drier and warmer boundary layer, which will
more rapidly entrain into the free atmosphere owing to the larger amount of sensible heat
supplied from below. This entrainment will further reduce the air humidity close to the
surface, to which vegetation often responds by a further reduction of the stomatal aperture
(Jacobs, 1994). These feedback mechanisms obviously have a pronounced effect on the
interaction between the surface and the atmosphere, and thus on the atmospheric response
to surface characteristics.
The implications of the feedback mechanisms for the exchange between the surface
and the atmosphere on a regional scale have been made clear by use of simple concepts to
describe PBL-dynamics and surface fluxes. For instance, De Bruin (1983) coupled a simple
slab model for the convective PBL (Driedonks, 1981) to the Penman-Monteith combination
equation providing surface fluxes. He showed that the the ratio of the surface evaporation to
the so-called equilibrium evaporation (Priestley and Taylor, 1972) depends on the surface
resistance for water vapour transfer, entrainment of heat from above the PBL, and
aerodynamic surface characteristics. Monteith (1995a) explored the accomodation between
transpiration from vegetation and the convective boundary layer by use of a similar model
for the PBL and a linear response of stomatal conductance to ambient humidity.
McNaughton and Jarvis (1983) introduced the concept of a 'coupling factor' fl, to indicate
the degree of interaction between a (vegetated) surface and the atmosphere. A strong
interaction is present when the aerodynamic exchange occurs very efficient, or when the
surface resistance is large.
Only for a constant surface forcing, both in time and space, the PBL will eventually be
completely adapted to the underlying surface. Adaptation to spatially heterogeneous
surfaces depends on the scale of the surface inhomogeneities. Hypothetically, fluxes from
small scale heterogeneities are blended at the scale of the boundary layer, but the PBL will
adjust to the local surface when the scale of the heterogeneities is large enough (De Bruin,
1987; Shuttleworth, 1988). Raupach (1991) pointed out that a PBL is rarely fully adapted to
the underlying surface, due to the relatively short time scale of the change of the lower
boundary conditions associated with the diurnal variation. This scale consideration provides
a second justification for considering surface-atmosphere interaction by using coupled
surface-PBL models to simulate surface boundary conditions for large scale modelling
purposes (Brutsaert, 1986).
These conceptual studies reveal the significance of land-atmosphere interactions, but
their results are not directly applicable as surface forcing in GCM's or NWP models. For these
applications a large range of parameterization schemes have been developed in the last two
decades. In the next section we will pay attention to these schemes.
1. Introduction 13
1.2 Land surfaces and land-surface models
The experiments listed above clearly demonstrate the need for a realistic land surface
parameterization scheme in meteorological models. The surface energy balance equation is
widely used to provide the lower boundary condition for atmospheric modelling purposes:
Qt = H + XE + G (1.1)
Here, Q» is the net radiation absorbed by the surface, H and XE are the sensible and latent
heat released to the atmosphere, respectively, and G is the heat stored in the ground and
surface elements, such as vegetation. A list of all symbols and acronymns can be found in
Appendix I. In eq. 1.1 the radiation term is defined positive downwards, while the
remaining terms are defined positive when directed away from the surface. Small amounts
of energy used for photosynthesis or other chemical processes are ignored and excluded
from this equation. Eq. 1.1 states that the total amount of radiative energy that is absorbed
by the Earth's surface is used to heat the air, to heat the soil, or to evaporate liquid water
that is a source of latent heat that can be used to heat higher atmospheric layers, when
condensation of evaporated water vapour occurs.
The amount of radiative energy absorbed by the surface, or its partitioning over the
terms on the right hand side of eq. 1.1, is importantly determined by the type of surface. For
polar regions covered with fresh snow a large part of the incoming shortwave radiation will
be reflected, leaving relatively little energy that can be used to melt ice (incorporated in G)
or heat the air aloft. A bare dry soil will show a quick increase of its temperature when Q» is
positive due to the absence of available water that can be evaporated. The low thermal
conductivity of a bare dry soil will result in a relatively small heat loss to G, and the surface
will thus release most of its energy as sensible heat (Oke, 1978). When vegetation is present,
it allows a significant energy release as latent heat, due to its capacity to transport water
from deeper soil layers via the root system. However, the water transport capacity of most
vegetation types is limited, and a vegetated surface will also act as a source of sensible heat.
Many micrometeorological studies have been dedicated to the description of the
energy balance for vegetated surfaces. A very well known concept is the so-called T ig leaf'
model (Monteith, 1965), that regulates the partitioning of available energy (Q. - G) over
sensible and latent heat by means of a series of transport resistances, which are governed by
both aerodynamic and plant physiological characteristics. Using such scheme a surface must
be characterized by parameters describing its aerodynamic roughness (Thorn, 1975),
radiative properties (Goudriaan, 1977) and physiological resistance for evaporation (Kelliher
et al, 1995).
Parameterizations using the simple big-leaf concept are often based on detailed
modelling and measurement studies of the microclimate within a canopy. Even for
horizontally homogeneous vegetation covers a significant vertical variation of radiation,
temperature or moisture exists within a vegetation stand. Multi-layer models describing
these gradients (see e.g. Waggoner and Reifsnyder, 1968) require often too much input data
and computation time to be useful in GCM's. Single layer models are more useful for this
purpose, as made clear in a — suggestively entitled — paper by Raupach and Finnigan (1988).
The simple 'big leaf' concept appears to lack realism in cases where the vegetation
• 14 Sparse canopy parameterizations for meteorological models
structure becomes more complex, for example, if the surface is only partially covered with
plants. In this case, a major part of the available radiative energy reaches the bare soil and
contributes to additional processes as heating of the underlying ground or of the air close to
it. This heating leads to interaction between the heat fluxes from the canopy and bare soil
components, in particular in cases where the canopy resistance is a function of ambient
temperature or air humidity. Furthermore, canopy evaporation is generally smaller than that
of fully vegetated surfaces as a result of the reduced leaf area. These surface types are
denoted as sparse canopies. Agricultural crops early in the growing season, natural vegetation
in dune landscape, tundra or savannah, or permanent orchards or vineyards in semi-arid
areas are general and widespread examples of sparse canopies.
Black et al. (1970) were probably the first to present a surface model computing the
evaporation from a surface that was only partially covered with vegetation. A few years
later, Deardorff (1978) presented a so-called two-component land surface scheme. In this
approach, the energy balance of a surface is split into a canopy and a bare soil component.
Deardorff's model was the first Soil-Vegetation-Atmosphere-Transfer (SVAT) model that
could be applied in large scale meteorological models. Since then several SVAT's were
developed which either regarded the Earth's surface as a single layer with various surface
components (Noilhan and Planton, 1989), or proposed major improvements to Deardorff's
model (Dickinson et al., 1986), or applied the Penman-Monteith combination equation to a
similar two-component scheme (Shuttleworth and Wallace, 1985). Apart from these papers,
numerous surface schemes were proposed that adapted one of these models for specific
conditions or modified the complexity of these schemes to either the simpler or more
complicated end (e.g. Sellers et al., 1986; Warrilow et al., 1986; Choudhury and Monteith,
1988; Shuttleworth and Gurney, 1990; Xue et al., 1991; Koster and Suarez, 1992; Dickinson et
al., 1993; Dolman, 1993; Braud et al, 1995; Viterbo and Beljaars, 1995; Bosilovich and Sun,
1995).
This abundant number of surface schemes provokes the call for intercomparison
experiments. Various studies have been dedicated to comparing several of these surface
schemes at various temporal and spatial scales. For instance, Dolman and Wallace (1991),
Inclân and Forkel (1995) and Huntingford et al. (1995) compared various SVAT's with ranging
complexity in a zero-dimensional mode, that is, by simulating fluxes using atmospheric
forcings measured close above the surface. At the global scale, Sato et al. (1989) and Sud et al.
(1990) compared the impact of replacing a very simple bucket hydrological model (Manabe,
1969) by the sophisticated Simple Biosphere (SIB) model (Sellers et al, 1986). The
aforementioned review of Mintz (1984) compares the sensitivity analysis of Shukla and
Mintz (1982) to a similar experiment conducted by Suarez and Arakawa (cited by Mintz,
1984) (and found considerable differences in continental rainfall for some areas). Recently,
the Project for Intercomparison of Land surface Parameterization Schemes (PILPS;
Henderson-Sellers et al, 1993; 1995) has been started, designed for a systematic
intercomparison of about thirty surface schemes that are operational in current GCM's or
NWP models. PILPS foresees in an extensive model documentation, sensitivity tests, and
intercomparison experiments ranging from zero-dimensional model runs, using both
synthetic and really measured forcings, to runs using fully coupled 3-dimensional global
scale meteorological models.
1. Introduction 1 5 •
1.3 A sensitivity analysis using a coupled SVAT-PBL model
Comparison experiments have shown that considerable differences exist between
surface fluxes simulated by different SVAT's. GCM and NWP simulations are shown to be
particularly sensitive to the parameterization of moisture transfer from deeper soil layers to
the atmosphere (Henderson-Sellers et al, 1995), and the treatment of this transfer is executed
rather differently by the various models.
An important question — one that is also one of the research topics in this thesis —
that arises is what level of complexity a land surface scheme must contain (Garratt, 1992,
1993). The large scale GCM or NWP sensitivity simulations contain so many degrees of
freedom that the results are often difficult to interpret, and can only be expressed in very
general terms. On the other hand, the stand-alone verifications of the various surface models
using in situ observations allow a more transparent evaluation of aspects that play a key role
in the exchange processes between the land surface and the atmosphere (and should be
parameterized well in meteorological models). A disadvantage of these zero-dimensional
intercomparison experiments is that atmospheric feedback processes cannot be taken into
account, and their results seem to depend strongly on the test conditions and input data
chosen. Furthermore, the number of processes that is simulated — even in relatively simple
surface schemes as Deardorff (1978) — is still large enough to inhibit a straightforward
interpretation of results.
In order to answer the question about the required level of model complexity, the
drawbacks of both the large global scale and small zero-dimensional comparison studies
should be avoided optimally. The strategy that is adopted in the current study is to consider
surface-atmosphere interaction using a coupled one-dimensional SVAT-PBL model. The single
dimension of the analysis allows a focus on the surface exchange processes, and disregards
large scale atmospheric effects as horizontal advection, cloud formation, radiation
penetration through the air mass, precipitation and other synoptic events. By considering
the transport of momentum, latent and sensible heat in a vertical column with a height
exceeding the typical PBL-height, surface-atmosphere feedback processes are allowed to
modify the surface fluxes.
Within this one-dimensional framework a range of surface models of varying
complexity will be coupled to a model for the PBL, and its response evaluated by performing
simulations over a specified surface. Parameterizations are compared that currently are used
in large scale meteorological models. This strategy differs in two ways from the PBL-
sensitivity experiments conducted by for instance Troen and Mahrt (1986) or Jacobs and de
Bruin (1992), who altered the lower boundary condition of a coupled surface-PBL model by
changing some of the surface parameters (albedo, crop resistance or fraction of potential
evaporation, aerodynamic roughness length):
(1) the interactions between surface and atmosphere are investigated for a specified surface,
rather than studying the effect of changing the land surface itself
(2) different existing parameterization schemes for land surfaces will be coupled to a
selected PBL-model, rather than that the sensitivity of one selected SVAT to the values
of the model parameters or input data is considered.
16 Sparse canopy parameterizations for meteorological models
A further attempt to focus on the physical exchange processes is carrried out by
disentangling the various parameterizations of the surface models. The various processes
that play a role in a land-surface parameterization scheme show many mutual interactions.
For instance, suppose that a certain SVAT that is used to calculate the energy balance of a
sparsely vegetated surface under conditions of strong radiation, describes an erroneously
small transport of water within the soil. Under the specified conditions, the bare soil surface
will soon dry out, which shows up as a strong increase of the soil surface temperature,
which affects net radiation and reduces the aerodynamic resistance owing to a stability
correction, which perhaps enhances the evaporation from the canopy component, which will
lead to an increase of the atmospheric humidity, etcetera. A sensitivity study will only be
able to compare various soil water transport modules if these are implemented in an
identical reference framework that describes the aerodynamic resistance, net radiation,
canopy fluxes etcetera.
In this study, we coupled a reference SVAT to a PBL-model, and four — more or less
isolated — parts of this SVAT are replaced with parameterizations taken from other land
surface schemes. The SVAT components that are distinguished and the reason for their
selection are:
(1) the representation of an incomplete vegetation cover. A crucial issue in the complexity of
land surface schemes is the importance of discerning between bare soil and
vegetation, in terms of surface temperature, radiation absorption and latent and
sensible heat exchange
(2) the type of soil model used. Various degrees of complexity are in use with respect to the
number of soil layers and the parameterization of heat and moisture fluxes within
the soil
(3) the aerodynamic exchange between the surface and the atmosphere. Apart from selection
of appropriate aerodynamic surface characteristics, a range of parameterizations can
be applied to account for the turbulent exchange efficiency
(4) the canopy resistance for evaporation. Not only the value of a minimum canopy
resistance can be specified according to the type of present vegetation, also the
complexity of crop resistance models varies widely.
Most of the parameterizations of these components are taken from models that have
been published in literature. We feel that the range of existing SVAT's is large enough, and
the development of new schemes should be based on an evaluation of existing material. The
results of the strategy of replacing model components will partly depend on the choice of
the reference model and the simulated surface. The coupling between various surface
processes will be different for different ways of representing surface processes or types of
surfaces.
As discussed before, the representation of sparsely vegetated areas induces stronger
demands on land-surface parameterization than closed canopies. The applicability of the
big-leaf model for dense vegetation covers has been demonstrated successfully, if the
surface resistance for evaporation can be well defined. A larger discrepancy between various
models is expected for sparse canopies, and these therefore serve as a better test
environment for our purpose. Sparse canopies form a common surface type in semi-arid
1. Introduction 1 7 •
areas, where the limited amount of available water constrains the biomass growth. A second
reason for focusing on sparse canopy surfaces is that, at the time when this project was
started, relatively little was known about the energy balance of a sparse canopy surface.
Since then, considerable work on this issue has been published, and these studies have been
useful here.
For the current study, a well-defined sparse canopy surface is selected to serve as test
case. This surface is a sparsely vegetated vineyard in a Mediterranean climate zone in La
Mancha, Spain, which was one of the investigated sites during the regional scale EFEDA
experiment (Bolle et al., 1993). EFEDA focussed on the surface energy balance of various types
of vegetation covers in the Mediterranean summer season, during which the evaporative
fraction of the surface available energy decreased considerably for many vegetation types.
This change of the surface energy balance enabled the verification of measurement and
modelling techniques in a large evaporation range in semi-arid conditions. Relevant for the
current study are data for calibrating the surface models, providing initial and temporal
forcings, as well as verification material. In the framework of this thesis these data were
collected during two measurement campaigns conducted in the summer growing seasons in
1991 and 1994.
The central aims of this thesis are:
(1) to provide insight in the physical processes governing the transport of momentum and
sensible and latent heat between a sparsely vegetated (Mediterranean) vineyard
canopy and the overlying atmosphere
(2) to compare existing land surface parameterization schemes for this particular dataset
with respect to the simulation of these fluxes
(3) to evaluate the sensitivity of the Planetary Boundary Layer to modifications of the land
surface parameterization scheme.
1.4 Organization of the thesis
This thesis pays attention to various aspects of (Mediterranean) sparse canopies, land
surface and PBL schemes and their intercomparisons. In chapter 2 the case study area is
described. A setup of the EFEDA project is discussed, and the site layout and measurements
collected in the Spanish vineyard area are presented. Special care was dedicated to existing
theory concerning corrections to measured quantities, in particular eddy-correlation. An
outline of the correction algorithms applied is included in one of the appendices to this
thesis.
Chapter 3 contains a survey of some processes governing the exchange between a
sparsely vegetated surface and the overlying atmosphere. It discusses the implementation of
sophisticated Lagrangian theory in the traditional aerodynamic exchange resistances, and
the shortwave reflectance (or albedo) of the case study area, illustrated by measurements.
Also discussed is the crop resistance for evaporation, where attention is focussed on the
application of a photosynthesis model for describing crop resistance (Jacobs, 1994).
Chapter 4 presents an overview of the land surface schemes and PBL model that are
selected for this analysis. The included surface models are selected in order to cover a
certain range of complexity with respect to aerodynamic transfer, soil heat and moisture
• 18 Sparse canopy parameterizations for meteorological models
transport, and surface representation. Selected are a form of the 'big leaf' model (Monteith 1965), and the earlier mentioned models of Deardorff (1978), Choudhury and Monteith (1988), and Viterbo and Beljaars (1995). The selected range could arbitrarily have been extended, but encompasses the desired range of possible parameterizations. Both single- and dual source models are included, as are differences in treatment of soil heat flow, aerodynamic exchange and canopy resistance. Also, special attention is paid to a small modification of the model of Viterbo and Beljaars (1995), which results in a clear improvement of flux predictions under some conditions. For the range of canopy resistance models the schemes of Choudhury and Monteith (1988) and Viterbo and Beljaars (1995) were chosen. Also included here is an operational version of the photosynthesis-resistance model of Jacobs (1994). A description of the latter canopy resistance model is included in chapter 3. The boundary layer model that was selected is originally developed by Troen and Mahrt (1986), modified by a convective closure scheme proposed by Holtslag and Moeng (1991). This is the same model as was used for the work carried out by Jacobs and de Bruin (1992) and Jacobs (1994).
In chapter 5 three land surface models that describe surface fluxes by explicitly discerning between vegetation and bare soil (Deardorff, 1978; Choudhury and Monteith, 1988; Viterbo and Beljaars, 1995) are compared by means of a five day simulation of EFEDA measurements collected during the 1991 campaign. This comparison is zero-dimensional, which implies that forcings measured at screen height were used as boundary conditions. The intercomparison focusses on the aerodynamic transfer and sensible heat flux, the soil heat flux, and the canopy evaporation and soil moisture budget.
Based on this comparison the SVAT components are selected that provide an optimum description of the observations. From these different components a reference model is constructed, for use in the coupled sensitivity runs reported in chapter 6. The coupled SVAT-PBL model is run for two artificial sets of initial and temporal boundary conditions separately. Components of the reference SVAT are replaced as outlined above, and the response of the boundary layer to this exchange is discussed. The PBL-response is evaluated in terms of surface and entrainment fluxes, mixed layer height, -temperature and -specific humidity. After this set of artificial simulations, measured initial and temporal boundary conditions are applied to the coupled SVAT-PBL model, in order to evaluate its skill to reproduce the actually measured meteorological conditions. This time the PBL-response is evaluated relative to a model run using measured surface fluxes as lower boundary conditions. The conclusion section of chapter 6 discusses the results, and presents suggestions regarding the sensitivity of the PBL to the parameterization of the land surface fluxes over a sparsely vegetated Mediterranean vineyard canopy.
1. Introduction 19
2 To measure is to know
(for what unknowns to correct for)
Data collection and processing
This chapter addresses the collection and processing of the data, used for this study.
The data presented in this chapter were collected in the context of the so-called EFEDA-
project, of which purpose and context will be explained first. Also the correspondence
between the EFEDA-purpose and that of this study is discussed. Then, the contribution of the
Wageningen Department of Meteorology to two EFEDA-measurement campaigns is
presented, including a description of the measurement sites. The data collection strategy is
discussed, where methods for determination of scalar and momentum flux densities,
available radiative energy, soil heat flux density, and vegetation parameters are adressed
separately. Finally, some quantities derived from the described measurements are
presented: aerodynamic roughness, roughness length for heat, soil thermal properties and
energy balance components.
2.1 The EFEDA-experiments
2.1.1 Context and goal
Since long mankind has influenced its environment. In Europe, land surfaces have
been transformed by human agricultural activities, as well as by the development of cities,
modern industries and traffic. These effects have gained special interest in the context of
climate changes induced by the greenhouse effect, as predicted by GCM's. Particularly at the
regional scale, model predictions of effects of change in global climate show large
differences. These are partially caused by inadequate parameterizations of the interaction
between the land surface and the atmosphere (Garratt, 1993).
In this context the Commission of the European Communities have developed the
European project on Climatic and Hydrological Interactions between the Vegetation, the
Atmosphere and the Land Surface (ECHIVAL), as an important component of the European
Programme on Climate and Natural Hazards (EPOCH). The first major activity of the
• 20 Sparse canopy parameterizations for meteorological models
programme was the ECHIVAL Field Experiment in a Desertification-threatened Area (EFEDA).
The main goal of EFEDA was to "get a better understanding of the processes, including the
impact of mankind, that may lead to land degradation and desertification" (Bolle et al., 1993).
More specifically, studies were carried out addressing the interaction between the
vegetation, the soil below and the atmosphere above at regional scales, compatible with the
grid scale of GCM's. Better parameterizations of these interactions are to be included in these
large scale models, in order to improve their predictive power. Earlier GCM-results showed
that the Mediterranean area is one of the most vulnerable European regions in case of a
progressing greenhouse effect. Therefore, and for reasons of orographical simplicity, EFEDA-
activities were concentrated in the relatively flat area of Castilla-La Mancha in Spain, in the
dry period of the growing season. Observations of the hydrological cycle, atmospheric
processes, vegetation development and soil properties were collected in a wide range of
spatial (from cm to 100 km) and temporal (from 0.1 s to 3 months) scales. Furthermore,
evaluation of data supports modelling activities, ranging from one-dimensional SVAT models
to three-dimensional mesoscale models.
The EFEDA-programme was split into two parts. The first part (EFEDA-I) consisted of
an intensive measurement campaign in the area of Castilla-La Mancha in June 1991, and a
first step towards linking the surface measurements to regional scale processes using
satellite images, airplane measurements and modelling activities. The project period was
limited to 2Vi years. EFEDA-II was funded for 2Vi more years mainly to execute additional
data processing and modelling. Furthermore, a few smaller experiments were carried out in
order to survey particular instrumental differences and repeat some of the measurements
carried out during EFEDA-I. The latter part of EFEDA-II took place in June-July 1994.
2.1.2 EFEDA-I
The spatial configuration of the ground-truth data collected during EFEDA consisted
of three 'supersites', at mutual distances of about 70 km: Tomelloso, Belmonte and Barrax
(Figure 2.1). Each of these supersites was considered representative for larger areas with
similar landuse. Tomelloso (39°10'N, 3°1'W, 670 m) represented unirrigated vineyards,
Belmonte (39°34'N, 2°27'W, 800 m) hilly natural and unirrigated agricultural vegetation, and
Barrax (39°3'N, 2°6'W, 700 m) both irrigated and unirrigated farm land, respectively. At
each of these supersites atmospheric, soil and vegetation data were collected at a number of
sites simultaneously. Airplane measurements played a key role in linking surface
measurements to the regional scale. Four airplanes were available, of which two carried flux
measurement equipment, and two carried remote sensing instruments.
About 30 scientific groups contributed to EFEDA-I. In the Tomelloso area continuous
measurements of the energy balance components, vegetation characteristics and soil
properties were collected at 9 sites by 7 groups, at typical mutual distances of 3-5 km. The
Department of Meteorology of the Wageningen Agricultural University (WAUMET)
coordinated and participated the collection of atmospheric and vegetation data in the
Tomelloso supersite. A further description of the collection strategy is given below.
2. Data collection and processing 2 1
Cs.
40 N
\39N
•
4W
Toledo
3W 2W
Cuenca
• -
Belmonte
•
Tortelloso • • Barra.'
m . * CiudadReal Alb loste
Figure 2.1: Geographic location of the EFEDA-area
2.1.3 EFEDA-II
EFEDA-II allowed some follow-up activities with respect to data processing, archiving
and measuring. Important gaps in the dataset of EFEDA-I were the availability of soil
moisture data in the entire rooting zone in the Tomelloso vineyard area, and a poor
coverage of the airborne flux measurements, especially the three-dimensional distribution of
the latent and sensible heat flux densities in the boundary layer. Apart from this, a number
of groups felt it necessary to reconfirm some issues noticed during EFEDA-I by additional
measurements. In this context a few participating groups decided to carry out a second
observation session in the Tomelloso area. Again airplane flux measurements were carried
out, together with a limited number (3) of ground stations. Also, WAUMET participated by
contributing to a single ground flux station, in close collaboration with the Wageningen
Winand Staring Centre (WSC) and the Copenhagen University (COP). A site close to
Tomelloso, which had been under investigation during EFEDA-I as well, was selected. For
EFEDA-II, data were collected during two months (June-July) in 1994.
Unfortunately, a planned measurement scheme of horizontal, vertical and temporal
variations of the soil moisture content was cancelled just before the experiment was
undertaken, due to problems with customs administration. Despite of this major lack of the
goal of EFEDA-II, the planned experiment was continued.
Apart from the routine flux measurements, two instrumental intercomparison
experiments were carried out in EFEDA-II. A net radiometer intercomparison was conducted
for ten days in June 1994 at a bare soil site near Tomelloso, and 10 sets of eddy-correlation
equipment were intercompared for ten days in May 1994 in Swifterbant, the Netherlands.
WAUMET coordinated the latter experiment.
22 Sparse canopy parameterizations for meteorological models
2.1.4 Correspondence of goals The goal and setup of the EFEDA-project fit very well in the current thesis. Similar to
the EFEDA-goals, the importance and skill of various surface-atmosphere interaction schemes for predictions at larger scales is under study here. Furthermore, EFEDA provides a framework for the collection of data necessary for evaluation of the various surface layer models. As indicated before, these models were to be evaluated under dry sparse-canopy conditions, with limited orographic influence.
A second aspect of the EFEDA-project which was very convenient, was that all participants agreed on mutual use of collected data. By this collaboration structure, data collected by other groups than WAUMET could be used for the present work. This particularly applies to the radiosoundings, collected by the Centre National de Récherche Météorologique (CNRM) of Toulouse, and the soil moisture data from the Dept. of Water Resources from the Wageningen University (WAUHBH). An overview of all surface flux data collected during EFEDA-I can be found in Chapter 5 of the Final EFEDA-report (Van den Hurk and De Bruin, 1993).
Measurements taken by WAUMET during EFEDA-I (1991)
2.2.1 Site description The site where WAUMET collected data during EFEDA-I was situated in a vineyard
near Tomelloso (39°08'30"N, 2°55'48"W, 693 m ASL), Castilla-La Mancha, Spain (see Figure 2.1). The prevailing wind directions were E and W. The surface type was almost homogeneous for a distance exceeding 1 km in both directions. Particularly in eastern directions the terrain slightly sloped, and height differences of about 5 m over a horizontal distance of a few 100 m were present. Approximately 15 km more southward the terrain was hilly.
The vegetation at the site consisted of grape vine plants (Vitis Vinifera. L. cv. Airen), placed in a regular grid of about 2.6 x 2.6 m. The plants had an age of about 50 years, and consisted of low stems (± 30 cm), from which early in the measurement season only a few minor branches emerged. Each branch carried 10-50 leaves, which are light green and hairy on emergence, darker, flat and with an area of ± 70-100 cm2 in their full-grown stage, and dark green, stiff and irregularly shaped by damage when they are old (see also section 3.4). Due to night frost prior to the experimental period the vegetative development was somewhat delayed. During June 1991, the plants grew considerably, both in height and in diameter, and developed ovaries. The growing stage was not completely ended by the end of the campaign. This canopy type covered approximately 80% of the area within the direct surroundings of the measurement site. Apart from vineyards, arable crops, bare soil and a small fraction of irrigated maize was found.
The soil was classified as a sandy loam soil with a fine texture. A large fraction was covered with stones with an average diameter of ± 3 cm. Due to a high iron oxide content the soil was red. At a depth of approximately 30 cm a zone consisting of hard, compact calcarous material was present. Investigations carried out in 1994 revealed that this layer extended to several meters depth, and not only a few decimeters, as was thought originally. A deep rooting zone enabled the vine plants to obtain water from the compact layer, which
2. Data collection and processing 2 3 •
has a large porosity. The upper soil layer was virtually dry during most of the period, and hardly any low vegetation developed.
Once every 3-4 weeks the vineyard was cultivated, to remove bits of weed and to loosen the upper layer. Moreover, during the growing season shoots who did not bear ovaries were removed manually. The harvest of the vine grapes occurred mid October. This type of land use could be considered typical for an extensive area of at least 100 km2 in the direct surroundings.
505 900 506 300
4 332 550
A
N
4 332 150
• 0
fallow land * — -P
vineyard
^ ~ l i \ - ~ - - - - * »
\.V-r_..-
S \
• \ t \ • \
/ • u
J m I V
• k ~ —
• d
a » # » b c
m~m m
f • •
g
^87Sm)
q
vineyard
Figure 2.2: site layout and urc-coordinates during EFEDA-I. Grid lines indicate a distance of 100 m. Labels are explained in Table 2.1
2.2.2 General set-up of WAUMET The main task of WAUMET was to collect data of scalar and momentum flux densities
between the vegetated surface and the atmosphere. In the period 2-29 June 1991 seven triangular masts (with diameter 0.20 m) were installed. Furthermore, soil measurements were carried out, together with the operation of a scintillation device, a SODAR device (both
24 Sparse canopy parameterizations for meteorological models
operated by the Royal Netherlands Meteorological Organisation, KNMI as subcontractor) and
radiometric surface thermometers moved horizontally along two cables at some height
above the surface (operated by sub-contractor Free University of Amsterdam, vu). Synoptic
observations were carried out hourly, whereas various relevant vegetation parameters were
collected throughout the entire month. An extensive project description is given by Michels
and Moene (1991). Here only a summary is given.
All automatic sensors were logged on a home-made datalogger controlled by a PDP-
11 minicomputer situated in a van at the site. Raw data were stored on magnetic tape,
copied to optical disk and processed afterwards. Eventually a tape had to be changed every
7-8 hours. From 7 June onwards, software adaptations allowed tapes to run for 17 hours.
Power for the measurement and processing system was supplied by a 220V generator,
located next to the van. The sampling frequency was 1 Hz for most sensors. The fast
response sensors were sampled mostly at 10 Hz. At some days the sampling frequency for
these sensors was increased to 100 Hz, since the generator was suspected to introduce a
significant 50 Hz noise on these signals. Under these conditions, tapes lasted for only 2Vi hrs.
Changing a tape took normally about 10 minutes, during which no data could be collected.
Early in the period only daytime data were available. Thunderstorms frequently
caused instrumental damage, even without any direct strike. Sensors were disconnected
from the datalogger when thunderstorms were nearby. Later in the period these storms
showed up less frequently, enabling more overnight measurements. Maintenance activities
were another source of gaps in the data sequence.
A second goal of WAUMET was to test a stand-alone flux station, which was being
developed for use in the Hydrological Atmospheric Pilot Experiment HAPEX-Sahel
experiment in Niger, 1992 (Goutorbe et al., 1994). Two Campbell 21X dataloggers were used
rather than the PDP-device in the measuring van. The station included a one-dimensional
sonic anemometer (Kaijo Denki DATllO) with a home-made thermocouple and Lyman-a fast
response humidity sensor, and standard wind-profile, Bowen-raho and radiation devices.
The energy was provided by solar panels. This station was operated from 9 June 1991
onwards. Data of this station were not used for the present study, and an extensive
description is not given.
Table 2.1 gives an overview of all sensors being in operation during EFEDA-I,
grouped according to the mast in which they were mounted. Figure 2.2 gives a site layout.
In addition, Bolle et al. (1993) present a photograph of the measurement site, taken in the
second measurement week. The following sections describe the sensors used and the
sampling strategy operated during EFEDA-I. A presentation of correction procedures applied
to raw data is given in Appendix II.
All data collected during this EFEDA-I campaign by WAUMET are stored in a database
(Krikke, 1994a). Surface flux measurements from all participants of EFEDA-I are collected in a
database prepared by colleagues from CNRM, and were disseminated on CD-ROM
(Anonymous, 1994).
2. Data collection and processing 2 5
Table 2.1: Instruments in operation during EFEDA-I; the indicated distance refers to the mast, the angle to the orientation with respect to the North
mast
a.
b .
c.
d.
e.
f.
g-
profile mast
aT mast
sonic mast
13 m mast
radiation mast
VU mast
VU eddy mast
sensor
5 psychrometers East-side
5 psychrometers West-side
wind vane
5 thermocouples
5 cup anemometers
wind vane
sonic anemometer
Lyman-a
thermocouple
net radiometer (above plant)
sonic anemometer
Lyman-a
thermocouple
net radiometer (above soil)
incoming shortwave pyrheliometer
reflected shortwave (plant)
reflected shortwave (bare soil)
infrared thermometer
6 C02-sampling tubes
8 cup anemometers East-side
7 cup anemometers West-side
incoming shortwave pyrheliometer
reflected shortwave (high)
net radiometer
wind vane
sonic anemometer
Lyman-a
thermocouple
type
home-made (PT100)
home-made (PTlOO)
home-made
home-made (CuCo)
home-made
home-made
Kaijo Denki DAT310
home-made
home-made (CuCo)
Middleton
Kaijo Denki DAT310
home-made
home-made (CuCo)
Middleton
Kipp CM5
Kipp CM5
Kipp CM5
Heimann KT14
vu-made
VU-made
Kipp CM5
Kipp CM5
Middleton
home-made
Kaijo Denki DAT310
vu-made
home-made (CuCo)
height/depth (m)
0.71,1.42,2.93, 4.93, 9.93
0.69,1.50,2.98, 5.04,9.98
10.20
0.67,1.47,2.95, 4.94,9.87
0.70,1.48,2.94, 4.93,9.86
10.20
4.35
4.42
4.40
1.07
12.50
12.50
12.50
1.03
1.30
1.07
1.05
4.20
0.5,1,2,4,12,21 4
0.5,1, 2, 4, 8,12,16, 21
1 ,2,4,8,12,16,21
6
6
6
21
4
4
4
distance (m)
0.85
0.90
0
1.35
0.90
0
0
0
0
1.10
0
0
0
1.15
1.65
1.65
0.78
0.30
3
3
3
3
3
3
0
0
0
0
angle
O 70
285
-155
95
-0-360 *
0-360 *
0-360 l
240
0-360 *
0-360 l
0-360a
170
245
245
120
195 2
3
3
3
3
3
3
-3
3
3
26 Sparse canopy parameterizations for meteorological models
mast
h.
' •
j -
k.
1.
m
n.
o.
P-
q-
stand-alone mast
Heimann mast
Diffuse mast
Stephenson screen
soil plot
cable high
cable low
SODAR
Scintillometer
soil plot (stand- alone)
sensor
wind vane
1-dim. sonic anemometer
Lyman-a
thermocouple
thermocouple
4 cup anemometers
net radiometer
incoming shortwave pyrheliometer
2 psychrometers
infrared thermometer (plant)
infrared thermometer (soil)
diffuse shortwave pyrheliometer
Assman psychrometer, min. and max. thermometer
incoming longwave pyrgeometer
5 soil thermometers (under plant)
5 soil thermometers (under bare soil)
3 soil heat flux plates (under plant)
3 soil heat flux plates (under soil)
4 Xp-needles (under plant)
4 A^needles (under bare soil)
moving infrared thermometer
moving infrared thermometer
SODAR
Scintillometer (over distance of 875 m)
soil thermometer (under plant)
soil thermometer (under bare soil)
type
home-made
Kaijo Denki DATllO
home-made
home-made (CuCo)
home-made (CuCo)
home-made
Middleton
Kipp CM5
home-made (PT100)
Heimann KT15
Heimann KT15
Kipp CM5
Assman
Eppley PIR
home-made (PT100)
home-made (PT100)
TPD Delft
TPD Delft
home-made
home-made
3
3
KNMI
home-made (PTlOO)
home-made (PTlOO)
height/depth (m)
6.00
4.13
4.14
4.04
2.05
0.90,1.50,2.96,4.94
1.30
1.30
0.75,2.00
0.97
0.91
2.00
2.00
2.00 6
-0.03, -0.05, -0.10, -0.25, -0.50
-0.03, -0.05, -0.10, -0.25, -0.50
-0.05, -0.05,
-0.05, -0.05,
-0.03, -0.05, -0.20
-0.03, -0.12, -0.35
6.00
3.00
-4 7
-0.03
-0.03
-0.15
-0.15
-0.10,
-0.22,
distance (m)
0
0.90
0.90
0.90
1.35
0.90
1.03
0.85
0.75
0
0
0
-
-
-
-
-
-
-
-
-
--
-
-
angle
(°)
-
140-220 1
140-220 a
140-220 1
295
350
170
205
120
190 5
190 5
-
-
-
-
-
-
-
-
-
-
--
-
-
2. Data collection and processing 27
mast sensor
soil heat flux plate (under plant)
soil heat flux plate (under soil)
r. measuring van and power generator
s. wsc-tower
t. wsc-albedo sensor
u. wsc-albedo sensor
V. TDR-plot
type
TPD Delft
TPD Delft
height/depth (m)
-0.05
-0.05
distance (m)
-
-
angle (°)
-
-
Sonics were adjusted to the wind direction regularly 2 the infrared thermometer had an inclination of -45° with the horizontal 3 complete information about exact configuration is not available 4 the upper sampling tube was used to measure the absolute concentration, the rest were measured differentially
against this level 5 the infrared thermometers had an inclination of -57° with the horizontal 6 placed on top of the Stevenson screen 7 The height of the scintillometer is not exactly defined, as the underlying surface is not entirely flat
2.2.3 Determination of available radiative energy
• Shortwave radiation
Three terms of shortwave radiation (0.3 - 3 |jm) were measured during EFEDA-I:
incoming total, incoming diffuse and reflected total. For all these components Kipp CM5
pyrheliometers were used, consisting of a thermopile, shielded by a double dome filtering
light outside this range. Incoming total shortwave radiation (K ) was measured at three
places (see Table 2.1): in the radiation mast, in the VU mast, and in the stand-alone mast. The
former two values were averaged to yield the best estimate of the incoming shortwave
radiation.
The diffuse radiometer was supplied with a solar shadow ring, which had to be
adjusted once every few days as the declination between the Earth's rotation axis and the
orbit plane changed. Early in the period the ring was not put in its proper position.
Comparison with data collected at a neighbouring site by WSC enabled selection of time slots
in which erroneous measurements were taken. Values in these time slots were rejected. T The reflected shortwave radiation, K , was measured at three places as well: over a
parcel of bare soil, over a plant, and at 6 m height in the VU mast. The exact position of a
downward looking sensor is of great influence for the amount of received reflected
shortwave radiation. Apart from differences in reflection coefficient between the plants and
the bare soil, local differences in soil humidity, iron content and plant density dictate a large
variability in the observed albedo, a (section 3.3).
• Longwave radiation From 18 June onwards an Eppley PIR longwave pyrgeometer was installed on top of
the Stephenson screen (see Table 2.1). By an internal body temperature measurement, the
instrument automatically corrects for the amount of longwave radiation being emitted by
itself. Only this corrected total incoming longwave radiation, L , was registered.
• 28 Sparse canopy parameterizations for meteorological models
Furthermore, the radiometric surface temperature was measured at a number of
locations. A fixed Heimann KT14 was mounted at 4 m height on top of the radiation mast,
looking downward at an angle of 45°. The sensor was mounted in a white PVC housing
preventing it from heating errors, and supplied with a narrow view angle lens (4°). The
instrument determines the radiometric surface temperature by measuring the longwave
radiation in a band, where the emissivity of the emitting surface is high and the contribution
of atmospheric radiation is low. Generally, surface temperature is measured in the range
between 8 and 14 urn. Two newer Heimann KT15 with a 16° view angle objective were
installed near the stand-alone mast: one above a parcel of bare soil, and one above an
individual vine plant. The temperature measurements from these sensors were also used for
the present thesis. These three sensors were calibrated in Wageningen before the
experiment. Calibration was carried out by measuring the sensor signal given by a
blackened cylinder (with longwave emissivity e = 1) in a water bath with known
temperature.
Also, at two locations a 8-14 (am radiometric surface temperature sensor was moved
along a cable of ± 30 m long, at 6 m height and at 3 m height (Van de Griend et al., 1989).
Both transects lead over a number of vine plants, separated by stretches of bare soil. A
transect was run every 10 minutes, but the sensor crossed the distance in approximately 200
s. Every 2 s a measurement was taken, which corresponds to a spatial resolution of
approximately 30 cm. A Campbell 21X datalogger triggered the start of each transect and
registered the measured temperatures. The strategy to obtain the average surface
temperature is outlined in Appendix II.
• Net radiation
During EFEDA-I net radiation was measured with four Funk radiometers manu
factured by Middleton (CSIRO). The heart of the sensor is a copper-constantan thermopile
between two blackened rectangular plates. On either side a thin (0.05 mm) poly-ethylene
hemisphere, transparent in both the longwave (3 - 3000 yon) and shortwave (0.3 - 3 urn)
range must be inflated by dry nitrogen gas, to avoid wind speed dependence of the sensor.
The instrument gives the total net radiation rather than separate upward and downward
components. Results from two net radiometers are used in this study, one situated 1 m over
a parcel of bare soil, and one at 1 m overhead the surface with a vine plant underneath. The
net radiometer at 6 m height in the vu-mast was not considered to give representative
readings due to mast shading, whereas the one used in the stand-alone station was regularly
used for net radiometer intercomparisons (see below).
An independent assessment of the net radiation is obtained by considering the
surface radiation balance, expressed as
Qt=(l-a)Kl+Ll-esoYlr <21>
in which T sur is an 'effective' surface temperature, defined as a area weighted average of
the plant and bare soil temperature (Blyth and Dolman, 1995). Incoming and reflected
shortwave radiation was measured directly, as well as the incoming longwave radiation
from 18 June onwards. The upward longwave radiation can be obtained from the
2. Data collection and processing 2 9 •
radiometric surface temperature, provided that the longwave emissivity of the emitting
plant and soil surfaces is known. However, to compare a radiation balance obtained in this
way with the measurement from a net radiometer introduces the difficulty in determining
the contribution of the several different surface elements to the radiation budget at that
particular position. Both albedo and radiometric surface temperature vary widely from
space to space, and particularly differences between plants and bare soil are large. The net
radiation measured at one height does agree with eq. 2.1 only when the surface emissivity
and the effective surface temperature are well defined, and when the radiative flux is
constant with height. The agreement is expected to be better early in the season, when the
plants still have a limited size. For Q, as obtained using eq. 2.1, T sur was derived from the
high cable (Appendix II), and a was taken constant, as discussed in section 3.3.
Apart from the decision of where to place the sensor, a major difficulty with net
radiation measurement is the accuracy of the instrument itself. Halldin and Lindroth (1992)
investigated 6 types of net radiometers, including a Funk-type. Differences of up to 10%
between different types of radiometers are not exceptional. This was confirmed by a brief
intercomparison experiment carried out at a bare soil site near Tomelloso, at a number of
days, and with a number of device configurations (Malhi and Van den Hurk, 1992). Sensors
of identical makes gave quite satisfactory correspondence, but instruments of the Funk or
REBS-type gave approximately 10% lower values than devices which separately measure the
upward and downward radiative flux density, as for instance the actively ventilated
Schülze-Däke. Particularly calibration of the longwave response is rather difficult.
Furthermore, the cosine response of the sensor is not perfect, underestimating the received
radiation at large zenith angles. Excess heating of the thermopile can result in a convective
heat loss, which is larger in the top dome than in the bottom dome due to the influence of
convection on air stability within the domes. For these reasons the accuracy of the Funk-type
instruments applied during EFEDA-I is believed to be no better than 10%, rather than the 5%
calibration accuracy specified by the manufacturer.
2.2.4 Determination of scalar and momentum flux densities
One of the key issues of the EFEDA projects is the assessment of the partition of
available energy over latent, sensible and soil heat, and the role vegetation plays in this
partition. The flux density of momentum is an important parameter for evaluation of the
aerodynamic exchange of scalars, such as C0 2 , heat or water vapour. Therefore, much
emphasis is put on the measurement of the momentum, sensible and latent heat flux
density.
The flux densities of scalars and momentum can be obtained using several methods.
All the methods employed here have the following assumption in common:
• ideally no distortion of the flow is caused by the measurement device
• the measured fluxes, being representative for the upwind terrain, can be related to the
locally measured available energy. This implies that the upwind terrain must be
homogeneous at a large enough fetch to ensure that the measured fluxes can be
considered to originate from that type of terrain only.
During EFEDA-I four types of measurements were employed for most quantities: eddy-
correlation, variance and scintillation methods, profile and Bowen-ratio methods.
• 3 0 Sparse canopy parameterizations for meteorological models
• The eddy-correlation measurements
The instantaneous vertical transport of a scalar with concentration p is given by the
product of px and the vertical wind speed w. A flux density averaged over a certain time
interval, Fx, is obtained by averaging w px:
r ~l~r (2 2) tx = Wpx = W p x + IV px ****'
where the right-hand side of eq. 2.2 is obtained by Reynolds averaging. In eq. 2.2 overbars
denote time averages, whereas primes denote deviations. The turbulent flux density is
defined as the transport perpendicular to the mean wind. In that case w = 0, and Fx is given
by w px. The flux density of sensible heat H is given by -pc w'%', where 9 is the potential
temperature, p is the dry air density, and c the specific heat of dry air. A latent heat flux —7~~7 dens i ty XE is equal to -pXw q , w i th q t he specific humid i ty a nd X t he latent hea t of
vapor iza t ion. The m o m e n t u m flux densi ty T is puw w i t h u t he horizontal w i nd speed,
whi le a flux densi ty of scalar c (for instance, a specific concentrat ion of C 0 2 ) , Fc is -pw'c' ( in
the following both the terms 'flux' and 'flux density' will be used simultaneously to denote
the transport of a constituent through a horizontal plane of unit area per unit time).
The eddy-correlation method requires measurements of w and x at a high enough
rate to include all the fluctuations contributing to the turbulent flux density. This highest
frequency is determined by the small-scale transition from turbulent eddy exchange to
exchange determined by the molecular diffusivity of air. The low frequency end of the
turbulent velocity range depends on the long term variations of the concentration and wind
speed, usually forced by diurnal variation or instationarity caused by large scale weather
systems. The turbulent transport takes place in the frequency range between these two
limits, in the so-called inertial subrange (Tennekes and Lumley, 1972). In the surface layer
this range is generally located between 10 and 0.001 Hz. Atmospheric stability and height
affect this frequency range, giving relatively more important contributions from smaller
time scales as height decreases or stability increases. Sensors that meet the frequency criteria
of the method are needed.
For wind speed, sonic anemometry is widely used. The wind speed in any direction
is measured by observing the difference of travel time of a sound pulse travelling over a
fixed distance in both directions parallel to the wind. The distance must be short enough to
be able to measure at a high enough frequency rate, but large enough to ensure time
measurement accuracy and to avoid flow distortion. The Kaijo Denki DAT310 uses an
averaging path of 20 cm, and measures the wind speed in three directions: u and v are
situated in the horizontal plane, and w is the vertical component. The transducers for the
vertical wind component are outside the measuring volume for the two orthogonal
horizontal directions. The DATllO measures the vertical component only.
Temperature fluctuations can be measured accurately with thin fast response
thermocouples. A thermocouple uses the temperature dependence of a potential difference
over a junction of two different materials, usually copper and constantan. The junction must
be fine enough to ensure a high response rate and reduce radiation heating of the wires. It
also needs to be strong enough to withstand most environmental features (wind, rain, dust).
The thermocouples used here are described by Van Asselt et al. (1991).
2. Data collection and processing 3 1 •
Sonic anemometry (Schotanus et ah, 1983) provides an alternative for fast response
temperature measurement. The sound propagation speed Vc depends on absolute air
temperature T and specific humidity q according to
v] = 403 T (1+0.51 q) ( 2-3)
The value of Vc can be measured by adding the transit times of the sound pulse travelling in
both directions between the transducers at a known distance. A sonic temperature T is
defined as
T _ Vc (2.4) son 4 0 3
Due to the dependence of Vc on q, Tsm (= T(l + 0.51^)) resembles but is not exactly equal to
the virtual temperature Tv, given by T/{1 - (1 - 0.622)e/p] ~ T(l + 0.61q), in which e and p are
the vapour and air pressure, respectively.
Fast response humidity fluctuations are usually measured using an optical method.
Water vapour absorbs light in certain wave frequency bands. The choice of the frequency
band should avoid the possibility that light is absorbed by other gasses, specifically oxygen
and ozone. The bands commonly used are Lyman-a at 121.56 nm and Krypton at 123.58 ran
in the ultra-violet, and some bands in the near-infrared (Buck, 1976; Tillman, 1991).
Measuring the intensity I of a monochromatic light beam passing through an open path of
length ds enables the determination of the amount of absorbing gas pv in the volume, using
Beer's law:
I = I0exp(-d$pvkv/pv0) (2-5)
Here, I0 is the beam intensity when pv = 0, kv is the absorption coefficient at standard
pressure, and p^ the (fictitious) water vapour concentration at standard pressure (1013 mb,
T = 0°C). A slight inconveniency is the fact that the response of I to pv is logarithmic rather
than linear. However, when the fluctuations I' are small relative to the average I, a
linearization of the response can be carried out, since then ln(l + I'/1)~I'/I, and pv' ~
-i/kvdsr/T. During EFEDA-I eddy-correlation measurements were carried out at 4 stations. Table
2.2 gives an overview of the configuration of each. At the stand-alone station (system 3) a
one-dimensional Kaijo Denki DATllO, including a home-made thermocouple and Lyman-a
device were operated. Three 3-dimensional Kaijo Denki DAT310 devices were operational,
also completed with home-made thermocouples and Lyman-a humidity sensors. Figure 2.3
gives an overview of the orientation of the different configurations. The Lyman-a's in the
lower masts (systems 1, 3 and 4) gave poor results throughout the entire measurement
period. Results from these sensors are left unconsidered. The two devices of systems 1 and 2
were rotated towards the mean wind regularly, to reduce flow distortion to a minimum. The
device of system 4 was left in a fixed orientation, but its data are not included in the current
study.
• 32 Sparse canopy parameterizations for meteorological models
Table 2.2: Configuration of the 4 eddy-correlation systems as used during EFEDA-I
Parameter
Name of mast (Table 2.1)
sonic dimensions
height (m)
frequency (Hz)
low-pass filtering of œ-signal from 19 June onwards
system 1
eddy mast
3
4.35
10/100
yes
system 2
13m mast
3
12.50
10/100
yes
system 3
stand-alone
1
4.10
10
no
system 4
VU-eddy mast
3
4.00
10/100
yes
1 sampling frequency is 100 Hz at days 19, 21, 22, 23, 25 and 26. At other days it was 10 Hz
0 - 90 degrees
Systomi Systems System 4
W 90 -180 degrees W 90-180
Figure 2.3: configuration of 3-dimensional sonic systems. The arrows indicate the preferred wind angle
In order to reduce the effects of the 50 Hz noise invoked by the generator, all fast
response signals should be low-pass filtered at a frequency well below the noise. Due to a
limited availability of filters only the signals of the vertical wind speed of systems 1, 2 and 4
were low-pass filtered at 10 Hz, using 4rd order Chebychev filters from 19 June onwards.
Before this date no filtering was applied.
All Lyman-a's were calibrated in a controlled humidity chamber at KNMI prior to the
experiment. The path length of the Lyman-a of system 2 was regularly changed between 1
and 2.5 cm to optimize signal resolution. The thermocouples were calibrated at WAUMET
using a water bath of known temperature. The factory calibration was used for the sonic
anemometers, although an offset was detected when placing them in a closed box in
Wageningen after the experiment. This offset was subtracted from the measurements during
postprocessing.
Corrections regarding rotation of the wind field, frequency response of the
measuring system, contribution of buoyancy to vertical velocity and light absorbtion by
other gases are discussed in Appendix II.
• The variance method In a horizontally homogeneous atmospheric surface layer, Monin-Obukhov
similarity theory predicts a universal relationship between the variance of temperature,
2. Data collection and processing 33
humidity and wind speed on one hand, and a dimensionless stability parameter (z - d)/Lv
on the other (Panofsky and Dutton, 1984):
• / - c xl 1-C (z -d )
V / -1 /3
x2- L „ < 0
Lv>0
(2.6)
where x represents horizontal or vertical wind speed (u and w, respectively), temperature
(6) or specific humidity (q). x, = u, for both u and w, where u, is the friction velocity. 0* and
q» are given by -w 6 /ut and -w q /ut, respectively. In eq. 2.6, cxl, cx2 and c are universal
constants, and the plus sign refers to x = u or » , and the minus sign to x = 6 or <j. z
represents height, d the zero plane displacement, and the Monin-Obukhov length Lv is
specified as
(2.7) K^a7e7(i+o.6iwV)
where K is the Karman constant (taken to be 0.4), and g the gravity acceleration.
From eq. 2.6 the sensible heat flux is given by
11/2
H = pcr
Je ^3
^ n s
Kg(z - d) (l-cT2(z-d)/Lv
~(z-d)/Lv
(2.8)
Assuming that the transport mechanism for heat and water vapour is similar in the surface
layer, it can be shown (De Bruin et al., 1993) that XE is given by
XE = Xp o.
3/2 CT1
Kg(z - d) l-cT2(z-d)/Lv) 1/2
<z-d)/Lv
(2.9)
Temperature-, humidity- and wind-variance measurements were collected during
EFEDA-I. Temperature variance was measured with the fast response thermocouples and
sonic thermometers already listed above. Moreover, identical fast response thermocouples
were mounted at 5 levels between 0.75 and 10.00 m in the so-called o ^ mast (see Table 2.1
and Figure 2.2). For calculations of H and XE differences between oT (which were actually
measured) and a e were ignored. Humidity variance was measured using the Lyman-a
devices described above, and the same applies to the sonic wind parameters. au was also
measured with 2 x 5 cup anemometers (see Table 2.1). For x = u there is evidence that eq. 2.6
is not obeyed under unstable conditions due to boundary layer interaction (Panofsky et al.,
1977). The dependency of au/u, on both boundary layer depth z; and z/Lv was elaborated
by Van den Hurk and De Bruin (1995), using the data implied here.
As for ae, Monin-Obukhov similarity theory predicts that also the temperature
structure parameter CT can be defined as a unique function of (z - d)/Lv. CT is defined by
34 Sparse canopy parameterizations for meteorological models
2 <T(h)2 -T(r2)
2> CT = i f (2.10)
1 2/3 r12
where r is a space coordinate, r12 the distance between r2 and r2, and the angular brackets
denote a spatial average. Details can be found in Hill et al. (1992). For unstable conditions
this relationship reads (Wyngaard et al., 1971)
C2T(z-df/3 ( ,- -V2/3
e! l - c ( 2 - r f ) (2.11)
The sensible heat flux density H can be obtained from eq. 2.11 when the friction velocity and
the universal coefficients c ^ j and C j ^ are known. De Bruin et al. (1993) applied eq. 2.11
using CJJI = 4.9 and CJJ2 = 9.
CT can be measured using scintillometry. Temperature fluctuations cause
fluctuations of the refractive index of air. Measuring the fluctuation of the light intensity of a
beam transmitted over a horizontal path with known length, this refractive index can be
determined. In general, both temperature and humidity fluctuations will cause fluctuations
of the refractive index. For operations in the visible or near-infra red range and at large
Bowen ratios this humidity contribution can be neglected. The light intensity fluctuations
are then directly proportional to CT (Kohsiek, 1982).
The setup of EFEDA-I consisted of a scintillometer provided by the Dutch KNMI as
described by Monna et al. (1994). A Campbell 21X datalogger was used to store half hour
averages of the refractometer index. The receiver was at a distance of 875 m from the light
source (0.94 |jm) and at approximately 3.28 m above the local surface. The terrain between
the transmitter and the receiver was not exactly flat. The effective height (z - d) in eq. 2.11 is
the local height over the entire light path weighted by the sensitivity function of the optical
configuration. This function is a bell-shaped function that tapers off to zero at both ends of
the optical path. The local terrain height could only be estimated from maps and
photographs. For (z - d) a value of 4 ± 0.5 m was found, and this uncertainty adds an
uncertainty of 12% to the calculated flux density. A comparison of values of H obtained
from this device and from the eddy correlation method is given by De Bruin et al. (1995) (see
also section 2.4.3).
• Profile measurements
The turbulent transport of heat, momentum, water vapour or any other scalar
between the surface and the atmosphere aloft is often described using a turbulent diffusivity
K, having the same meaning as a molecular diffusivity for laminar flow:
2. Data collection and processing 3 5
. , T, 08 H--pcrK»!ï
XE = -Xp Ke dz
PKm^ 3ü
3z (2.12)
Fc = - P ^ C
de
3z
In eq. 2.12 c is defined as the specific C02-concentration/ equivalent to q. In the surface layer
the values of the turbulent diffusivity depend on local height, friction velocity and stability.
For K, Dyer and Hicks (1970) proposed
\ l / 2
Km = K « , 2 • 1 6 - 1
J
Kh=*e Kc = K U . Z 1-16 — L„
1/4 (2.13)
for unstable conditions, and
Km=Kh=Ke=Kc = Ku,z 1 + 5 . -1
(2.14)
for stable conditions. Paulson (1970) derived expressions for the stability corrections in eqs.
2.13 and 2.14 in integrated form.
During EFEDA-I the turbulent flux densities of momentum, sensible and latent heat
and C 0 2 were determined using eq. 2.12 and measured profiles of u, 9 and q and C0 2 .
Five wind profiles were measured (see Table 2.1): in the stand-alone mast at four
levels, in the o^-mast at 5, in the profile mast at 5, and in the high VU-mast at 7 and 8 levels,
respectively. Measurements from the vu-mast were discarded due to poor calibration
reliability of the cup anemometers. The sensors of the stand-alone mast were also left out of
the present analysis. The two remaining profiles were measured using home-made cups
mounted on 0.90 m long booms at approximate levels 0.75,1.5, 3, 5 and 10 m and pointing to
approximately East (o^-mast) and West (profile mast). A selection of either of these two
profiles was made using a wind vane placed on top of the profile mast (East profile selected
when the wind direction < 180°). The cup anemometers were calibrated in a wind tunnel in
Wageningen before installation in Spain.
The sensors appeared to be very sensitive to electrical charge fields induced by
lightning events. The long cable bridging the distance between the masts and the measuring
van enabled generation of large voltage differences between the electric poles of the sensors,
thereby destroying the electronic circuits. Even without any direct lightning strikes in any of
the masts, most cup anemometers were frequently out of order, particularly early in the
measurement period.
Three temperature and humidity profiles were measured using home-made
psychrometers: one in the stand-alone mast at 2 levels, and two times in the profile mast at 5
levels (see Table 2.1). Again, the stand-alone mast data are left out of consideration. The
psychrometers in the profile mast were mounted on booms of about 0.8 m length on both
36 Sparse canopy parameterizations for meteorological models
East and West side of the mast at each level. The psychrometer consisted of a dry bulb and
wet bulb temperature sensor (PTIOO) mounted in a ventilated housing with all-side radiation
shielding. Also the thermometers themselves were encased by a single metal radiation
shield, open at the bottom side. Air speed within the housing exceeded 6 m/s . Destilled
water was pumped actively to the wicks around the wet bulb sensor, and water surplus
dripped off. Dry bulb temperatures T were corrected for dry-adiabatic rise by adding 0.01 CC
per m above surface. This is a simplified correction obtained from the definition of potential R/c
temperature 6, given by T (p0/p) p, with p0 = 100000 Pa and R the molar gas constant. The
temperature profile was obtained by averaging the two dry-bulb temperatures at each level.
Vapour pressure e was obtained from the dry bulb T and wet bulb Tw from each
psychrometer using
e-es{Tw)-CjL(T-Tw) (2-15)
es(T) is the saturated water vapour pressure at temperature T (computed using
610.7 x io7-5TA237-3+T), T in °C), e = mv/ma = 0.622 with mv and mfl the molar weights of
water and dry air, respectively, and air pressure p ~ 94000 Pa was derived from the synoptic
observations (see below).
The psychrometers suffered from quick pollution of the wet wicks, in spite of
changing the wicks about twice a week. Moreover, the water supply was often insufficient
to guarantee the wicks to remain constantly wet. A third source of severe error was heating
of the instrument bottom caused by upward longwave and shortwave radiation. Since all
these errors would obviously lead to an overestimation of Tw, the humidity profile was
obtained by selecting the humidity measured with the psychrometer giving the lowest value
of Tw at each level. However, this procedure could not ensure that the measured profiles
were reliable. Later designs of the psychrometer (as applied during e.g. EFEDA-II) have
eliminated most errors.
u,, H and E were calculated simultaneously using the least squares technique of
Robinson (1962) and Covey (1963). This procedure minimizes the difference between the real
profiles of u, and T and a hypothetical one according to eq. 2.12, assuming a constant flux
throughout the entire profile. An iteration is necessary in order to include stability effects on
these profiles. The contribution of the water vapour flux to Lv was ignored here. Once «» and
H are found, E can be computed from the resulting value of «. and Lv, again minimizing the
difference between the real and a hypothetical profile of q. For computations of u», H and E
the lowest level (0.75 m) was excluded in every case, since this level was too close to the
individual plants to expect the flux density to be constant.
The C0 2 profile measurements were carried out by the members of the Free
University of Amsterdam (vu). Unfortunately, severe calibration difficulties of the C 0 2 gas
analyzers were caused by the high air temperatures, and the profile data could not be used
to calculate C02-fluxes. It was also decided to refrain from a detailed description of these
measurements.
• Bowen-ratio method
The Bowen-ratio method is a profile method which uses the assumption that the
2. Data collection and processing 3 7 •
transport mechanism for heat is equal to the transport mechanism for humidity, thus
Kh = Ke. Using this assumption the Bowen-ratio H/XE can be measured according to
ß = ü = S _ ^ | (2.16) A.E A, A Ö
Together with eq. 1.1 the individual terms H and XE can be computed when the total
available energy Q» - G is known.
During EFEDA-I the psychrometer measurements were also used to obtain values of
H and XE using this technique. A regression of a scatter plot of T vs. a yielded the best
estimate for AT/Aq (Sinclair et al., 1975), and again measurements at the lowest level were
not included.
2.2.5 Determination of soil heat flux density The soil heat flux density G is an important component of the energy balance for a
sparse canopy site. Simultaneously, the horizontal distribution of soil heat flux may show
considerable differences, caused by surface temperature differences, shading by plants,
presence of stones, or variability of soil texture and moisture content. G depends on various
soil physical properties and the temperature forcing at the surface. Verhoef et al. (1995)
discuss various methods to measure soil conductivity, soil heat capacity and soil heat flux
density, as applied during EFEDA-I. Here two methods used to measure the soil heat flux
density are briefly reported: the flux plate method and the heat capacity method.
The flux plate method uses flux plates consisting of a thermopile embedded in a heat
conducting material with a similar thermal conductivity as the ambient medium. The
thermopile results in a potential difference if the temperature at either side is different and a
heat flow is present. A calibration procedure transfers the voltage difference to an actual
heat transport. Major corrections to the heat fluxes determined using this method are
presented in Appendix II.
The heat capacity or caloric method measures the change of the heat content of a soil
profile between two subsequent time slots. The heat content C at time t of a soil profile is
given by
q t ) = ]p'Ch(z)T5(z,t)àz (2.17)
where p'Ch(z) is the volumetric heat capacity of the soil at depth z, and Ts(z, t) the soil
temperature at time t at the same level. The soil heat flux density at the surface is then given
by
_ at+At) ~ a t - A D ( 218) 2At
A continuous record of temperature data at a sufficient number of levels between the
surface and a depth where the soil heat flux density can be assumed negligible are
necessary. The temperature at the surface is important, since the major temperature changes
• 3 8 Sparse canopy parameterizations for meteorological models
occur near the heat source. During EFEDA-I the soil heat flux density under a parcel of bare
soil was computed using the (corrected) radiometric surface temperature measurements
(Appendix II). For the heat flux density under a plant the surface temperature was
approximated using a harmonic analysis of the soil temperature at 3 cm depth (van Wijk,
1963). The thermal diffusivity necessary for this method was obtained from measurements
of the soil temperature at various depths using the amplitude method (Horton et al., 1983;
see Verhoef et al., 1995). For this method the amplitude AT of the diurnal temperature cycle
with radial frequency q>T must be detected at two levels. The thermal diffusivity k of the soil
layer between these two levels is then estimated as
12
K 7 = — Zj-Z2 2 InliT.'T' -I / /\.rp ry
(2.19)
k was computed daily for the layers 0-3 cm, 3-5 cm, 5-10 cm, 10-25 cm and 25-50 cm, using
the temperature profile of the bare soil parcel completed with the radiometric surface
temperature, provided that the fundamental temperature cycle was measured completely, k
was assumed not to vary horizontally, thus at any depth being equal for the bare soil and
the soil under a plant. The temperature profiles were smoothed using a higher order spline
function evaluated at 40 equidistant levels between z = 0 and z = 50 cm depth (Press et al,
1986).
The volumetric soil heat capacity p'Ch appearing in eq. 2.17 is a function of the bulk
density of the soil, p', and the specific heat C of the various constituents in the soil, p ' is
given by
D = o x + o x + o x + o x (2.20) r rs*s rw w ran ^0 0
where xi is the relative fraction of constituent i, and the subscript w refers to water, s to soil
mineral, a to air and o to organic matter. xs + xw + xa + xg = 1, per definition. p'Ch is equal to
p'cfc-E*,P,c, (2-21)
For practical use paCfl = 0, and organic compounds are neglected. psCs = 2 MJ/m K, and
pwCw = 4.2M]/m3K.
During EFEDA-I six soil heat flux plates (TPD Delft) were in use: two at -5 cm under
bare soil, two at -5 cm under a plant, one at -15 cm under bare soil and one at -15 cm under
a plant. Furthermore, two temperature profiles of 5 PTlOO sensors between -3 and -50 cm
were installed, one of them under a parcel of bare soil and one underneath a plant (see Table
2.1). Soil porosity (1 - xs) and soil moisture content (xw) were measured by members of the
Dept. of Water Resources of the Wageningen University (Droogers et al., 1993). Soil porosity
was measured once during the campaign, and water content about once every 5 days, both
averaged over five 10 cm intervals between 0 and -50 cm. For this, Time Domain
Reflectometry (TDR) was used. The contribution of organic material was neglected. Detailed
soil moisture measurements were also carried out by colleagues of the Winand Staring
2. Data collection and processing 3 9 •
Centre, but these data are not used for the present thesis.
An important soil physical property is the thermal conductivity Xr = k p'Ch. During
EFEDA-I it was determined directly, using home-made socalled X^needles (Shiozawa and
Campbell, 1990). This instrument measures the rate of change of soil temperature nearby a
heating probe. The rate of temperature change and the distance between the heating element
and the temperature sensor depend on the heat conductivity of the soil surrounding the
probe. Eight needles were installed at various depths in the soil, again under plants and
under soil (see Table 2.1). The measurements were carried out manually using a Campbell
21X datalogger, who also regulated the heat supply to the probe. The measurements were
carried out approximately twice every campaign day.
The average soil heat flux density was obtained as a weighted average of the heat
flux density under bare soil and under a plant for each of the two methods. The fraction of
vegetated surface (Cy, section 2.2.6) was used as the weighting factor. Numerical simulations
showed that the influence of horizontal heat flow (induced by horizontal variations of the
surface temperature) on the heat flux measurements is limited.
2.2.6 Determination of vegetation parameters
The present vegetation is characterized by its physical dimensions (height, width of
canopy elements, leaf density), its relative evaporating surface (Leaf Area Index LAI) or
areal occupation (fraction of plant cover, oy), a canopy resistance for evaporation (rsc), and
some other features. Since the vegetation showed a significant growth during the measuring
period, most measurements have been carried out more than once. Table 2.3 lists the dates
at which the several determinations were carried out. All vegetation data presented here
were sampled on the right hand side of the terrain depicted in Figure 2.2. Vegetation
surrounding masts s and t in this figure was slightly less developed than in the
surroundings of the other masts due to a more severe frost damage which had occurred late
in April 1991. A detailed description of the determination of the vegetation parameters
during EFEDA-I is given by Michels and Moene (1991).
Table 2.3: Dates at which plant parameters were determined, and total number of sampled plants during EFEDA-I. Date numbers are days in June 1991
parameter
crop height ('traditional')
crop height (individual plants)
drip area
Leaf Area Index
stem height
stomatal resistance
dates
16, 20, 25
5, 9, 11,14,17, 20, 23, 28
16, 20, 25
5, 9, 11, 14, 17, 20, 23, 28
16 -20
15, 17, 19, 21, 22, 23, 25, 27, 28
number of plants
-10
5 (16, 20), 10 (25)
10
10
2 per sample
• Canopy height and plant dimensions The vine plants were sitated in a regular grid, ± 2.60 m apart. The resulting plant
density D was 0.15 plants/m2, valid for the entire field. The crop height h was measured in
two ways. By the first 'traditional' method h is assessed by looking over the canopy, and
• 4 0 Sparse canopy parameterizations for meteorological models
determine the average height. For a canopy consisting of widely separated plants the
method is rather subjective. Alternatively, the height of each plant from a sample of 10 was
measured. The crop height was defined as the 70% percentile value of this sample. A
cumulative frequency distribution showed a rather sharp increase of the cumulative
frequency at this percentile value (Michels and Moene, 1991). Figure 2.4 shows the resulting
values of h. Also shown is the estimated crop height before the measurement campaign. The
value at 5 June is suspiciously high. At this date, the sampling strategy was probably not yet
well-established, and changed afterwards.
Of these ten plants, also the stem height and stem diameter were measured once
(divided over two days).
1.2-|
1.0
I0'8"
£ 0.6->> a. o
« 0.4-
0.2-
o.o-
•
(-) •
- -• •
•
-
10 15 20 date (June 1991)
25 30
Figure 2.4: •: Canopy height h measured during EFEDA-I, where h is defined as a 70% percentile value of individual plant height measurements. The measurement taken at 5 June is suspiciously high and marked between brackets; • : the estimated canopy height before June 1991
The drip area Ad is the average surface area occupied by a single plant. It was
measured three times by assessing the horizontal diameter of 5 (first and second time) and
10 (third time) plants.
• Leaf Area Index and Leaf Area Distribution
The onesided Leaf Area Index (LAT) was obtained by estimating the total leaf area,
LA, of 10 plants. LAI, defined as the average leaf area per unit ground area, is then simply
given by
LAI = TAD „ (2.22)
An alternative expression for the amount of (onesided) leaf area is the average leaf area per
unit plant surface, LAI», equal to LAI/a* where Oris the fraction of surface covered with
vegetation (see below). This parameter is relevant to the description of radiative extinction
within the individual plant elements.
The detection of LAI was carried out 8 times (see Table 2.3). LA is computed as the
product of the number of leaves, N, and the average area A; of a selection of leaves from
each plant. N was counted manually, and a separate record was kept for each layer of 20 cm
2. Data collection and processing 41
height. No distinction was made between leaves in separate age classes or light regimes. The
average leaf area was also registered per layer, using the so-called vein method (Daughtry,
1990). For this method the length of both the primary and secondary vein of a random
sample of leaves is measured, and related to the true area of the leaves using a calibration
curve. The calibration is carried out by relating the product of the two vein lengths of a leaf
to its area, determined by counting the dots on a graph paper occupied by the leaf. This 'leaf
tracing method' was applied to a random selection of 99 leaves once early in the
measurement period. The measurement of LAI using this strategy took 2 to 4 days per run.
The day numbers listed in Table 2.3 refer to the centre of each run. Figure 2.5 shows the
resulting values of LAI.
Figure 2.5: • : Leaf Area Index (per unit ground surface) measured during EFEDA-I. Also shown is the linear regression, given by 0.0382 + 0.0127 day, where day is the day in June 1991
10 15 20 date (June 1991)
• Fraction of vegetation cover
The fraction of vegetation cover Oris the relative horizontal area occupied by
vegetation. When the average drip area Ad is known, it is easily obtained as Ad D . The
parameter plays an important role in the determination of the amount of radiation reaching
the surface, the surface albedo and other processes. During EFEDA-I Ad was measured only
three times, in a short time range (see Table 2.3). Due to the rapid growth of the vegetation
Oris expected to vary strongly and alternative ways to assess it are desired. Here Or was
obtained by a combination of measurements of LA, h and Ad, and adoption of two
assumptions:
• The leaf area density obtained from measurements of Ad is constant throughout the
period, since plants are expected to increase volume instead of density as leaf area
increases
• The plants can be described using a perfect ellipsoid based on the ground and with
equal radius rx = jAd I % in the two horizontal directions. This assumption is a little
different from Hicks (1973), who states that vine plants can accurately be described
by cylinders.
From rx and h the average volume V of a single plant can be computed using the
42 Sparse canopy parameterizations for meteorological models
description of an ellipsoid:
V = tn0.5hr2r
3 x (2.23)
The average leaf area density LAD, defined by LA/V, was found to be 6.3 m / m . From this
o"r is found from
. _, 2 _ 3 LAI a f = A, D„ = n rv D„ = ƒ à p x p 2 hLAD
(2.24)
'ƒ Figure 2.6 shows the resulting values of oy
0.15
o.io-
o.oo
Figure 2.6: • Fraction of surface covered with vegetation, o\> obtained using eq. 2.24;
0.0379 regression of a» given by 9 + 0.0011 day + 8.26 10"* day2
10 15 20 date (June 1991)
• Fraction of sunlit leaves During EFEDA-I the relative fractions of sunlit or shaded leaves and of the leaves of
the several age classes was not measured explicitly. The fraction of sunlit leaves, fs, was
eventually estimated using a numerical model adapted from Norman and Welles (1983).
They developed a scheme computing the path length of a beam from a specific direction
through an ellipsoidal canopy element with specific dimensions. This scheme was used to
compute the average sunlit area of a plant canopy as function of the spatial distribution of
plants, their geometrical dimensions, and the direction of the solar beam. The latter
parameter is a known function of season and time. fs is then obtained by
fs = exp(-kbldsLAD) (2.25)
where fcw is the extinction coefficient for black leaves, and ds the path length of a beam
between the leaf and the edge of the canopy element. Leaf area density LAD is assumed
constant over the canopy element volume. fcw was parameterized as 0.5/sinß (where ß is the
solar elevation), which applies to a canopy with spherically distributed leaves (Goudriaan,
1977). The average fraction of sunlit leaves is obtained from averaging the values of/s in a
grid box enclosing a single plant element. Taking LAD equal to 5 m 2 /m 3 , the resulting value
2. Data collection and processing 43
of/s was very well approached by a fixed value of 0.5 ± 0.1 for all times and days (figure not
shown).
• Stomatal resistance
Measuring stomatal resistance
The stomatal resistance rs( relates the transport rate of gases between a stoma and the
air directly surrounding the leaf to the concentration difference of the gas:
r = n Ci~°s (2.26)
Here, F is the flux density of the gas and c the gas concentration. The subscripts refer to
inside the stoma (i) and directly outside (s), respectively (Monteith, 1973). The stomatal
resistance is a measure for the pore width of the stomata in an individual plant leaf.
Table 2.4: Sampling details of porometry and photosynthesis measurements during EFEDA-I
parameter stomatal resistance photosynthesis
total number of days
time range per day
measurement frequency
number of plants per measurement
number of leaves per layer
leaf categories discerned:
• leaf layer (20 cm each)
• age
• light condition
• total
number of cycles per leaf
total number of samples
sunrise - sunset
once every two hours
2
3 -6
sunrise - sunset
once every two hours
1
5-10
3 (young, normal, old) 3 (young, normal, old)
3 (sunlit, shaded)
54
3
2317
intermediate, 3 (sunlit, intermediate shaded)
54
1
1469
A detailed description of the stomatal resistance measurements during EFEDA-I is
given by Jacobs (1994) and can be found in the final EFEDA-I report (Bolle and Streckenbach,
1993). Here only the basic elements are given.
On nine days the stomatal resistance was measured on a random set of plants. A
distinction was made between leaves in different layers (20 cm height each), light regime
(sunlit and shaded) and age categories (young, normal and old). Leaf age determination was
based on the size, thickness, colour, hairiness and regularity of the shape of the leaves. Table
2.4 lists the sampling details.
The stomatal resistance for water vapour transfer was measured using a dynamic
diffusion porometer (Delta-T Mk3), which measures the rate of increase of the relative
humidity in a cup of approximately 0.3 cm3 attached to a leaf. The relative humidity rh in
the cup will rise due to transpiration through the stomata and the cuticula. The instrument
44 Sparse canopy parameterizations for meteorological models
pumps dry air into the cup until a relative humidity rhs is reached, where rh$ is a start value
approximately equal to the ambient relative humidity. Then, the transit time At necessary to
increase rhs by a specified humidity change Arh is recorded. As soon as rh > rh$ + Arh, the
drying cycle restarts automatically. Usually Arh is set to 5%. At each leaf position Af was
recorded three times, after two or three drying cycles in order to achieve a stable value of At.
A single measurement took 15 - 45 s (depending on gs), which is considered short enough to
avoid adaptation of the leaf to the cup microclimate.
Ideally, At/Arh depends on rst = l/(gs + gcut) in a linear way, where gs is the stomatal
conductance and gcut the cuticular conductance of a leaf. The slope and offset of this
regression are determined by the cup dimensions and the diffusion coefficient for water
vapour. However, temperature differences between the cup and the leaf will affect the water
vapour transport speed. Monteith et al. (1988) derived expressions to correct for these
temperature differences, and these were applied (see also Jacobs, 1994). Furthermore, the
limited time response of the humidity sensor and temperature-dependent adsorption of
water vapour at the cup walls cause a deviation from the linear relationship between At and
l / (g s + gcut). These features make a calibration in the field necessary. Calibration was carried
out using a plate perforated with six sets of holes of known geometry, whose conductance
could be determined from theory. A new calibration was carried out for each measurement,
and a linear regression between Af and l / (g s + gcut), corrected for temperature difference,
was used.
Measurements of water vapour conductance on the abaxial side of the leaf (where no
stomata are present and thus gs = 0) gave no significant increase of the cup humidity. This
leads to the conclusion that the cuticular conductance gcut = 0, and it can be neglected
during further analysis.
Scaling up from leaf to crop
For the surface layer models forming the subject of this research, a crop resistance
against evaporation is required, rather than a stomatal resistance on a large number of leaf
surfaces. A weighted averaging is applied to obtain the crop resistance from the individual
leaf stomatal resistance data. The mean crop resistance rsc per unit ground area was
obtained following a LAJ-weighted averaging (Wallace et al, 1990)
LAI
i. ah'
S^1)
(2.27)
Since rs( significantly differed for different age classes and light conditions, the weighting
should reflect this as well. From the discrete number of leaf classes rf is given by
1
AI
Ei [E/ , J
-1
(2.28)
where/j represents the relative fraction of class i, and rst. is the average value of r$t of leaves
2. Data collection and processing 4 5 •
in class i. The averaging interval was one hour for all occasions. The discerned classes are
the sunlit and shaded leaves (specified by fs), the leaf age and the vertical position.
During EFEDA-I the value of fs was assumed equal to a fixed value of ± 0.5 for all
times and days. However, the measurements taken during EFEDA-II (see below) showed a
significant variation of fs as function of local time. Therefore the quadratic function shown in
Figure 2.9 was taken instead for EFEDA-I data.
The fractions of the various age classes were estimated to be distributed as 20%
young leaves, 40% normal and 40% old. Since the average resistance of young leaves is
generally much higher than the resistance of the normal and old leaves, a variation of 10%
of this figure results in a variation of only 4% of the crop resistance. The small difference
between the stomatal resistances of old leaves and normal leaves makes the exact estimation
of these fractions of minor importance.
The vertical leaf area distribution was measured directly during EFEDA-I.
• Photosynthetic rate
In the context of EFEDA-I the photosynthetic activity of the plants was also measured.
Results from these measurements were used to calibrate a model for gs based on the
computation of the net photosynthetic rate, An 0acobs, 1994; Jacobs et al, 1995; see also
section 3.4). A detailed description of these measurements can be found in Jacobs (1994),
while here only a basic description is given.
The photosynthetic activity of a leaf can be expressed in terms of the amount of C 0 2
being transported to the leaf. The C02-concentration cR of the air at a reference height above
the canopy (4 m) was measured using an Infra-Red Gas Analyzer (IRGA). The air was also
transported to a transparent cuvette clamped onto a leaf, and the C02-concentration c0 of the
air returned from the leaf cuvette was also measured. Then the photosynthetic rate An can
be calculated from the concentration difference (cR - c0), the air flow through the chamber
and the leaf area in the cuvette (Ball, 1987). A correction for the dilution of C 0 2 by the
addition of H 2 0 must be applied.
The sampling strategy resembled the strategy employed during the stomatal
resistance measurements (see Table 2.4). Only one instead of two plants was sampled each
measurement, but more leaves per sample layer were monitored.
2.2.7 Various determinations • SODAR
Between 1 June, 13.40 GMT and 29 June, 14.00 GMT a 3-dimensional doppler sodar
device was in operation at about 500 m from the WAUMET site (see Figure 2.2). The sodar
device was provided by the KNMI (Monna et al, 1994). Profiles of horizontal and vertical
wind speed and their standard deviations were detected at a resolution of 25 m between 50
and 500 m height, where the upper level depends on atmospheric conditions. The
instrument and datalogger were powered by a 220V generator at sufficient distance to avoid
distortion of the measurements caused by the sound of the generator. Data were stored as 20
minute averages. The system clock, however, depended on the generator frequency, and
showed a time accuracy of less than 5 min. The SODAR data were not analysed in the context
of this study.
• 4 6 Sparse canopy parameterizations for meteorological models
• Synoptic observations
During periods that the measuring van was in operation, synoptic observations were
carried out approximately every hour, according to the SYNOP-guide of the Dutch weather
service (KNMI, 1981) as close as possible. The parameters that were observed were:
• air pressure, measured with a hand held altometer, converted to pressure at sea level
using the hydrostatic pressure equation p(z) = p(0) exp(-g z/R T ), where T is the
average of the virtual temperature at z = 670 m and a virtual temperature at sea
level, equal to Tv - 0.01 z
• air temperature and air humidity with a ventilated Assman psychrometer in the
Stephenson screen (see Table 2.1)
• relative humidity with a hygrograph in the Stephenson screen
• maximum and minimum temperature in the Stephenson screen
• total cloud cover, fraction of low, middle and high clouds, and estimated height of
lowest cloud base
• codified state of weather.
Observations were noted in the WMO synoptic coding algorithm. Specifically, the
observations of air pressure were actually used for several corrections related to
thermodynamic properties of the air.
• Radiosoundings
During EFEDA-I the French CNRM carried out a total number of 93 radiosoundings
about 1500 m from the measuring site of WAUMET. These soundings were launched on each
day between 1 and 30 June 1991 at 11 GMT, and on some days every 2 hours. The balloons
were equipped with sensors reading air temperature, air humidity and air pressure. CNRM
made these data available to WAUMET.
For each sounding the boundary layer height z; was estimated as the level of the
lowest inversion of potential temperature and specific humidity. Driedonks (1982a) assumes
that the error of estimating zi from a single sounding is approximately 100 m, owing to a
considerable horizontal variation of the boundary layer height. Often obvious inversions
were observed at several levels below 5 km, as a result of the remaining residual boundary
layer from the period before. The estimated PBL-depth varied from 100 m to almost 4000 m.
Table 2.5 lists values of z,- observed at times where clear inversions were present. These
values were used in the analysis of oM-data by Van den Hurk and De Bruin (1995).
Measuremen t s taken b y WAUMET dur ing EFEDA-II (1994)
The second EFEDA-measurement campaign, taking place in June and July 1994, was a
joint experiment of the Wageningen Staring Centre (WSC), the Copenhagen University (COP)
and WAUMET. All three groups had participated to the EFEDA-I experiment, performing flux
measurements in the Tomelloso supersite.
2.3.1 General setup
A single set of equipment was composed from contributions of each group. Roughly
2. Data collection and processing 4 7 •
Table 2.5: Times of observations of lowest inversion heights and number of ground observation time slots
Day (June 1991) time (GMT) level of lowest inversion (m)
number of ground observations (30 min average)
7
9
9
11
11
12
21
22
23
25
25
26
26
27
28
28
28
29
29
total
11:30 -12:30
13:30 - 14:00
16:00 - 17:00
11:30 -12:30
13:30 -15:30
9:30 -10:00
13:00 -15:00
14:00 - 15:00
16:00 - 16:30
9:00 - 10:00
13:30 -14:30
8:00 - 8:30
12:00 - 15:00
12:00 - 15:00
8:00 - 10:30
12:00 - 12:30
14:00 - 14:30
9:00 - 9:30
15:00 - 17:00
890
2100
2520
1730
2200-2230
660
3100 - 3700
3450
3200
910
3850
500
3400 - 3450
2200 - 2450
500 - 750
1000
1500
700
2200 - 2300
2
1
2
2
3
1
2
2
1
2
2
1
3
3
5
1
1
1
2
37
spoken, WSC provided a complete eddy-correlation device, WAUMET the wind-, radiation-,
temperature and soil data, and COP a soil respiration-, sapflow- and porometry device. Table
2.6 lists the complete set of equipment. The stations of WAUMET and WSC were assembled
and tested during the eddy-correlation intercomparison experiment carried out in
Wageningen in May 1994.
Again, a vine site near Tomelloso was selected to install the equipment. Each of the
contributing groups operated the station for 3 weeks, and during a few days the take-over
by the different teams was organized.
Measurements were taken in the growing season of the vineplants, between 1 June
and 30 July 1994. No rainfall occurred during the measurement period. Information from
local landowners revealed that there had not been any rain fall for a month preceding the
measurement period. Since October 1993, only 50 mm precipitation had fallen in the area.
The eddy-correlation data were measured at a frequency of 10 Hz, and stored on a
hard disk of a portable PC in the field. The 'background'-data collected by the equipment of
WAUMET were logged on a Campbell 21X datalogger, and only half hour averages were
stored. Also sapflow data were collected once every half hour, on a Campbell CRlO
datalogger. All devices were powered with solar panels and batteries in the field. During the
experiment, almost instantaneous data control was allowed by daily computing mean
values and covariances of the eddy-correlation station and major corrections to all data
• 4 8 Sparse canopy parameterizations for meteorological models
Table 2.6: Equipment in use during EFEDA-II; the indicated distance refers to the mast, the angle to the orientation with respect to the North
mast
eddy-correlation
background station
instrument
3-dim. sonic anemometer
Krypton hygrometer
H 2 0 - and C02-gas analyzer
wind vane
4 cup anemometers
1 psychrometer
net radiometer
incoming shortwave pyrheliometer
reflected shortwave pyrheliometer
diffuse shortwave pyrheliometer
radiometric surface thermometer
type
Gill/Solent
Campbell KH20
LICOR6262
home-made
home-made
home-made
Schülze-Däke
Kipp CM5
Kipp CM5
Kipp CM5
Heimann KT15
height/depth (m)
6.00
6.00
6.00 l
10.57
2.96, 5.46, 7.48, 10.23
6.09
7.91
7.80
7.80
2.00
7.80
distance (m)
-
0.10
-
-
0.90
0.50
1.06
0.60
0.60
-
0.50
angle
(°)
-
360
-
-
360
360
180
250
250
-
250 2
soil measurement plot
rain meter
sap flow
8 soil heat flux plates
4 soil temperatures
rain gauge
3 sap flow gauges
csmo
home-made PTlOO
Dynagauge
4 x 0.01, 4 x 0.05
2 x 0.01, 2 x 0.05
0.30
1 whole stem 2 single branches
1 The height refers to the sample tube inlet 2 the Heimann was tilted at an angle of approximately 7°
using a software package developed in collaboration between WSC and WAUMET.
Just like during EFEDA-I, a C0 2 flux density was measured, but this time an eddy-
correlation method was used rather than the profile method. Also sapflow- and soil
respiration measurements were carried out. Results from these are not used for this study,
and are described by Friborg (1995).
Unlike EFEDA-I hardly any data collection interruptions occured. The systems proved
to be very reliable, and only little maintenance was necessary. Moreover, no threat of
thunderstorms was present this time.
2.3.2 Site description The vinesite of EFEDA-II (39°7'19.94" N, 2°55'18.55" W) resembled the EFEDA-I site in
most features. Again, a regular grid of plants was situated on a sandy loam soil covered
2. Data collection and processing 49
with stones. The plants were slightly wider separated (2.70 m), and were younger than the
plants found at the EFEDA-I site, about 20 years. Compared to that site the terrain was
somewhat more unevenly sloped, and the fetch was about 500 m in both East and West
conditions. (Inspection of the EFEDA-I site in 1994 revealed that much of the vineyards had
disappeared since 1991.) Figure 2.7 gives an overview of the terrain layout.
500 m Main road C40
Figure 2.7: Site layout during EFEDA-II; Left: general surroundings of measurement plots, where solid lines indicate (dirt) roads; Right: measurement plot details, where also shown are the locations where the plant parameters were sampled
2.3.3 Determination of available energy and surface temperature
• Shortwave radiation
During EFEDA-II the same components of shortwave radiation were measured as the
case for EFEDA-I, but each component only once. Both incoming and reflected shortwave
were measured with Kipp CM5-sensors at 8 m height above the surface, to obtain an albedo
representative for the combined surface and plants system. Calibration of all shortwave
radiation sensors was carried out at WAUMET shortly before installation in Spain. However,
the new calibration yielded almost identical results as the factory calibration, and the latter
set of calibration factors was adopted.
A diffuse radiometer was installed separately on a mast of 2 m (see Table 2.6). A
Kipp shadowring was used and installed according to its manual. About once every 5 days
the position of the shadowring was adjusted according to the sun's declination.
• Longwave radiation Neither the incoming or outgoing longwave radiation were measured directly during
50 Sparse canopy parameterizations for meteorological models
EFEDA-II. Rather, a two-sided allwave sensor (Schülze-Däke) mounted at 8 m height was
used. This sensor measures the airwave radiation (short- and longwave) by two thermopiles,
separated by a massive aluminium body. Also the body temperature is measured with a
PTlOO thermometer. A 0.1 mm thick dome of Lupolen-H eliminates wind speed dependence
and is self-supporting. An active wind stream over the outer side of the body housing and
domes is caused by a fan, and reduces differences between the temperature of the sensor
body and the surrounding air. Each of the two sensors is calibrated for the longwave and
shortwave sensitivity separately. The longwave radiation received by either sensor, L and
L , can be computed from a separate measurement of the shortwave radiation terms, K and
K , and the sensor body temperature Tb:
L U = A i . î _ K i . î + o T * (2.29)
where A and A are the measured allwave contributions in downward and upward
direction, respectively, and the longwave emissivity of the sensor is assumed to be unity.
Also, the surface temperature was measured using a single Heimann KT15 mounted
at approximately 8 m height. The view angle of the instrument was 16°, and the radius of
the circle being seen was therefore 4.6 m, large enough to cover bare soil and some plant
parts. The areal distribution of plants and soil in this view area is assumed to resemble the
true areal coverage.
Apart from the fixed sensor, at several days the surface temperature was observed
using a handheld Chinon device. The sensor was placed in several predefined positions over
individual plants and stretches of bare soil before reading the temperature. A total number
of eight plants was observed this way, where the overhead temperature of all plants was
recorded. Moreover, the temperature measured looking to four plants in Northern and
Eastern direction was registered, together with the temperature seen looking South and
West to the other four. The unshaded bare soil temperature was monitored at eight positions
in between the sampling plants. Also, the temperature of soil just Northern and Eastern of
four plants was measured, plus the soil just southern and western from the four others.
Table 2.7 gives a brief summary of the frequency of the handheld surface temperature
measurements.
• Net radiation The net radiation could only be obtained for the level at which the radiation sensors
were mounted, that is, 8 m. No distinction between plants and bare soil is made here. Net
radiation was calculated as the balance of the (corrected) values of incoming and reflected
shortwave and incoming and emitted longwave radiation.
2.3.4 Determination of scalar and momentum flux densities During EFEDA-II, momentum flux density was measured using both fast-response
eddy correlation measurements and the profile method. The results from the profile method
are not used here. The scalar flux densities (heat, water vapour and C02) were measured
using fast-response sensors only.
A three-dimensional Gill/Solent sonic anemometer at 6 m height formed the heart of
2. Data collection and processing 5 1 •
Table 2.7: Frequency of handheld surface temperature measurements
quantity number
Measuring days 173, 179,182,184,194, 202, 204, 205, 208
Measurements per day appr. every 2 hours
(sunrise - sunset)
plants per measurement 8
orientation: - overhead plant 8 - N, E, S, W side of plant 4 each - overhead bare soil 8 - soil N, E, S, W of plant 4 each
the eddy correlation station. Unlike the Kaijo Denki DAT310, u, v and w are measured in the
same volume.
No thermocouple was added to the system. A sonic temperature was obtained from
the vertical wind signal. WSC obtained experimental evidence for a reliable application of the
sonic temperature (corrected for humidity contributions, see Appendix II) for measuring the
sensible heat flux density from the earlier HAPEX-Sahel experiment in Niger in 1992. The
factory calibrations were used for all signals. The temperature signal, however, was
recalibrated using the temperature obtained from the psychrometer at 6 m.
Fast response humidity measurements were carried out with two devices: a
Campbell KR20 Krypton hygrometer, and a LICOR6262 closed path gas analyser. The factory
calibration of the Krypton appeared to be very stable, both the offset and the gain. An in situ
correction was applied to the calibration gain using data of the psychrometer at 6 m.
C 0 2 concentration fluctuations were measured with the LICOR6262 as well. Air is
pumped into a sample cell, and light absorption at two frequencies in the infra-red region is
used to detect the concentration of C0 2 and H 2 0 in the cell. A dry and C02-free reference
gas is created by a closed second air circuit which is pumped continuously through cristals
of magnesium perchlorate (hygroscopic) and soda lime (absorbing C02). Calibration of both
the offset and the gain of the two signals was carried out once every 10 days in the field
using dry nitrogen (zero), a dewpoint generator creating air with a known water vapour
concentration, and a bottle with air containing a known C02-concentration (227 ppm).
Appendix II lists the eddy-correlation corrections applied.
2.3.5 Soil measurements
• Soil heat flux density During EFEDA-II only the heat flux plate method was used to assess the soil heat flux
density. A total number of eight plates (CSIRO) was used, of which four were installed at 1
cm depth and four at 5 cm depth. The plates were placed in pairs above each other in a row
between two plants, such that the first two and last two were temporarily shaded by the
plants, and the others were under sunlit soil almost all day (see Figure 2.8). Sensor 8 was
logged single-ended, due to a limited number of datalogger channels. After the experiment,
the measured results of this sensor had to be discarded.
• 52 Sparse canopy parameterizations for meteorological models
Close to each of four flux plates a PTlOO soil thermometer was installed. Two PTlOO
sensors were buried at 1 and 5 cm under sunlit soil (near plates 3 and 4), and two at similar
depths near plates 7 and 8 (see Figure 2.8).
A
N G 3 4 ® Figure 2.8: Layout of soil measurement plot. G = soil heat flux plate, T = thermometer
• Soil physical parameters
No further soil physical parameters were collected in the field during the
measurement period. It was assumed that soil porosity was identical to the situation during
EFEDA-I. The water content in the top soil layer was very low during EFEDA-I (<8%), and this
figure was adopted here as well.
The hard lime layer below a depth of 50 cm turned out to extend for a considerable
depth, at least 4 m. The material was rather homogeneous and had a high porosity,
exceeding 50%. The soil moisture content throughout the layer varied somewhat, but was
estimated to be 12 m 3 /m 3 everywhere in the layer (Havercamp, personal communication).
2.3.6 Determination of vegetation parameters • Crop height, leaf area
In principal, during EFEDA-II identical methods were applied to assess crop height
and leaf area. The only change compared to EFEDA-I is reflected in the sample selection. 27
plants were now chosen to sample h and LAI. 25 of these plants were situated in a line
approximately East - West, starting at the measurement site (see Figure 2.7). From the start
point, every third plant was selected, thereby covering a line of approximately 250 m, which
was considered to yield a representative sample. Furthermore, two plants involved with sap
flow measurements were also sampled. As was evident from the statistical analysis of the
significance of the LAi-data measured during EFEDA-I, the period between two LAI-
measurements must be long enough to detect any change at all (Michels and Moene, 1991).
Therefore, the sampling frequency was reduced to once every 10 days. Table 2.8 specifies
dates and the number of samples used for the vegetation-measurements.
During EFEDA-II, the crop height h was defined as the 80% percentile of the
individual plant lengths. The frequency distribution of h showed a very gradual increase,
and the sharp increase at 70% observed during EFEDA-I was not present.
Jacobs (1994) did not find a significant dependence of stomatal resistance on height,
which made a specification of leaf area per vertical layer redundant. On the other hand, LAI
was specified per age class (young, normal and old). The calibration values to relate the vein
product to leaf area (section 2.2.6) were obtained from 100 leaves per age class as well. The
calibration was carried out three times, once every three weeks. Figure 2.9 shows the
2. Data collection and processing 5 3 •
Table 2.8: Dates at which plant parameters were determined, and total number of sampled plants during EFEDA-II. Date numbers are DOY in 1994
parameter
crop height
Leaf Area Index
calibration LAI
fraction of vegetation cover
stem height and diameter
fraction sunlit leaves
stomatal resistance
sampling days
152, 161, 168, 177, 185, 201, 207
152,161,169, 177, 185, 200, 2101
152,173, 210
152,161, 168,177, 185, 201, 207
153
165,188, 204
157,159,163, 166, 170,173,179, 182,184,188, 197, 198, 202, 205, 208
number of samples
27 plants
27 plants, 3 age categories: • young • normal • old
300 leaves
27
27
15
6 each day
1 Measurement days for LAI refer to centre of series of days to measure all plants
development of leaf area per age class during the measurement season. A higher order
polynomial was fitted through each of the age classes, to be used for the upscaling of
porometry measurements to canopy averages (section 3.4).
old • normal
young
0.25^
_ 0.20 1 f 0.15
0.10
0.05
0.00
fll l l • 1
152 161 169 177 185 200 210 daynumber
6 9 12 15 18 21 24 time (GMT)
Figure 2.9: Vegetation measurement results from EFEDA-II. Left: leaf area index per age class; Right: Fraction of sunlit leaf area measured at three days. Also shown is the quadratic function given by fs = 0.46(1 - [(t -12)/8] ), where t = time
• Fraction of sunlit leaves Since obviously leaf stomatal resistance depends on the light regime of the leaves,
the fraction of sunlit leaves, fs, is an important weighting factor to obtain crop resistance.
During EFEDA-I this was not measured explicitly, but was assumed to remain constant
during the day (see section 2.2.6). Here, this assumption was investigated by measuring the
fraction of sunlit leaves.
54 Sparse canopy parameterizations for meteorological models
The method consisted of counting of the number of leaves being sunlit standing
away from a plant, and to relate these countings to the total number of leaves of each plant,
as determined during a LAf-measurement session. The number of sunlit leaves was counted
on 15 plants approximately every two hours before noon, assuming a symmetric response
over the day. A distinction was made between three age categories. The method was applied
once every 20 days. Figure 2.9 shows the resulting values of fs. Also shown is an eye-fitted
quadratic function of time, which was used for the upscaling of stomatal resistance
measurements to the canopy scale.
• Fraction of vegetation cover
To determine the fraction of vegetation cover, Or, the plant radius of each sampling
plant was estimated as the mean of two perpendicular cross section diameters. The cross
sections were chosen to lie in the line of sampling plants and perpendicular to that line, over
the plant stems. The variation between the plants was very large due to the fact that
individual branches contributed to the cross section diameter to a large extent, in spite of
their small contribution to the real drip area. Results are shown in Figure 2.10.
0.20
0.15
! 0.10
0.05
0.00
Figure 2.10: a, as measured during EFEDA-II. The solid curve represents the best-fit polynomial regression, given by oy = 10.33 -0.18d»y + 9.9 lO^day2 - 1.81 lO^day3
170 180 190 Date (1994)
210
• Stomatal resistance Measurements
As during EFEDA-I, the stomatal resistance of the plant leaves was measured with a
dynamic diffusion porometer. This time, a newer version (DeltaT, Mk4) was used. The
difference with the previous version was a higher degree of automatic data processing.
Calibrations were carried out in the field as well, but immediately applied to the data
measured after the calibration. A correction for temperature differences between the cup
and the leaf (Monteith et al., 1988) was automatically employed.
During most of the 15 sampling days (see Table 2.8) leaf stomatal resistance was
measured from sunrise until sunset. A distinction was made between the three different leaf
age classes and two classes of radiation regime (shaded and sunlit), yielding a total number
of six leaf classes. Until day 173 (22 June) measurements on 18 leaves were equally
2. Data collection and processing 55
distributed over the six leaf classes, but later only four leaves were taken from the young
age class (two shaded, two sunlit) and eight from the intermediate age class. Each
measurement day, six plants were selected and sampled throughout the entire day: five
were selected randomly from the sample line of 25 plants, and one of the plants with a sap
flow shoe was always monitored. Measurements were taken nearly continuously during
daytime, which yielded approximately 50 leaves per hour (or 750 samples between sunrise
and sunset). Also the leaf temperature and the amount of incident Photosynthetic Active
Radiation (PAR), as measured with the porometer device, were logged and stored for further
analysis.
09:00 12:00 Urne (GMT)
4i>
40
? 1 | 35
30-
doy 208
• •
a
-
D/ -
a -
a
12:00 time (GMT)
Figure 2.11: Leaf temperature as obtained from (D) the porometer (averaged for both sunlit and shaded leaves) and (— »—) the manual radiometric surface temperature measurements. Horizontal lines represent one standard deviation from the average of the radiometric temperatures; Left: DOY 173; Right: DOY 208
Upscaling to the canopy scale
During EFEDA-II explicit measurements of fs and leaf area per age class were
available, while the porometry measurements were not divided into different height
intervals. The fitted functions of fs and LAI were used to average rst to canopy scale
resistances according to eq. 2.28.
Also hourly averages were computed from the leaf temperature measurements and
the amount of incident PAR, both for shaded and sunlit leaves separately. The leaf
temperature measurements were compared with the plant temperature readings obtained
from the manual plant surface temperature measurements (section 2.3.3). Figure 2.11 shows
the diurnal course of the average leaf temperatures obtained from the porometer and the
manual radiometric recordings for two days in 1994. Porometer readings were averaged
over sunlit and shaded leaves. The sunlit leaves were on the average 0.64 °C warmer
(t2 = 0.994). Also shown are the standard deviations of the manual measurements. The
agreement is satisfactory for the data shown. We conclude that the porometer values are
accurate enough to be used for calculations involving the stomatal resistance (section 3.4).
56 Sparse canopy parameterizations for meteorological models
2.4 Derived quantities
2.4.1 Aerodynamic roughness and displacement height
Aerodynamic roughness is an important parameter for the estimation of momentum
and scalar flux densities between the surface and the atmosphere. For sparse canopies the
aerodynamic properties are a complex function of plant geometry and size, roughness of the
bare soil, and distribution of canopy elements with height.
For EFEDA-I the aerodynamic roughness and displacement height have been
determined using various methods: the wind profile method, eddy-correlation
measurements, and a geometrical method. An additional method using eddy-correlation
measurements at various heights (Lloyd et al., 1992), was applied as well, but yielded results
that contained a scatter too large to be significant.
• Wind profile method
In the wind profile method, z0m and d are determined as integration coefficients of a
theoretical wind profile fitted to observations (Robinson, 1962). This optimalization
technique is in fact similar the the method for obtaining sensible heat and momentum flux
density from profile measurements (see section 2.2.4). The theoretical wind profile is found
by simultaneously solving for the displacement height d, roughness length z0m and friction
velocity u,. Stability corrections to this profile were included using eddy-correlation
observations of z/Lv, and the integrated functions of Paulson (1970). Representative values
of z0m and d are defined as the median of a sample of results. Since the vegetation grew
rapidly, results were grouped per period of approximately 5 days. Only time slots with
near-neutral values ofz/Lv (-0.1 <z/Lv< 0) were included, to minimize the impact of the
stability corrections. Measurements carried out by the lowest cup (0.75 m) were discarded.
Figure 2.12 shows the results of z0m and d for the EFEDA-I dataset, obtained by this
method. The roughness length is shown to increase significantly as the season proceeded,
but the displacement height derived from the profile method remained fairly constant, at a
value of about h/3 (also shown).
• Curve fit method using eddy-correlation measurements
An alternative computation of the most likely value of both z0m and d is proposed by
Jacobs and van Boxel (1988). Measurements of a sonic anemometer at a single height can be
used to specify a relationship between z0m and d. For a neutral surface layer these quantities
are related according to
z-d = exp
z0m
( \ KM
v"'
(2.30)
As before, z0m and d are also computed using a least square fitting technique. The
resulting values usually show a considerable scatter. The optimum value is found by
employing a linear regression through a scatter diagram of z0m and d, and seeking the
intersection with the line obtained by the eddy-correlation measurements, eq. 2.30. In fact,
this intersection replaces the assumption that the median of the sample determines the
optimal values of z0m and d. Resulting values of z0m and d for EFEDA-I are also shown in
2. Data collection and processing 5 7
Figure 2.12. They correspond well to the results obtained from the profile method.
0.08-
0.07'
0.06-
0.05-
fo.04-
0.03-
0.02-
0.01
0 1 1
J l | 1 l
-,
|
l 1 l f
^ _ ua-l profile H oa' I sonic + profile • 0.7 n Raupach
— °*
lllll'l 1-5 6-10 11-15 17-20 21-25 26«)
period (June 1991) 1-5 6-10 11-15 17-20 21-25 26-30
period (June 1991)
profile
sonic + profile
hf3 • Raupach
Figure 2.12: Measurements of roughness length (left) and displacement height (right) taken using various methods during EFEDA-I (see text)
• Geometrical method
Raupach (1992) developed a general theory about the total drag exerted by a rough
surface. The normalized roughness length z0m/h is a function of the roughness density (or
frontal area per unit ground area) r\ = b h/D , where b is the characteristic width of the
roughness elements, and D the horizontal spacing. z0m/h first increases with r\ until n = 0.3,
and decreases with a further increase of n. This picture was established by the one-
dimensional numerical second-order closure computations carried out by Shaw and Pereira
(1982). According to Raupach's theory the drag coefficient CM(z), given by
CMM = M ( 2 )
I In K
( \ z-d
0m \ P
can be computed from the relationship
u(h) •ih = (c. -nCR)-1 /2exp(cTiYA/2) (2.31)
where C s and CR are the drag coefficients of the unobstructed substrate and an isolated
roughness element, respectively, and c is a O(l) coefficient. Eq. 2.31 is an implicit
relationship in \ , but can be solved fairly easy. The roughness length is then found from
'0m h-d ™ =^J lexpOP)exp( -Ky h ) (2.32)
¥ is a profile influence function, accounting for the departure of the actual momentum
diffusivity profile from the surface layer profile K «» (z - d). The displacement height d is
defined as the centroid of the drag force profile, affected by both the roughness elements
and the underlying substrate. Raupach derived for d the expression
58 Sparse canopy parameterizations for meteorological models
ß*1 I l+ß R Tl
( \ ( V/2
* . .-1 M
(2.33)
)
where cd is a constant equal to 0.6, and ßR = CR / Cs.
Figure 2.12 shows the results for the EFEDA-I dataset. The width of the canopy
elements, b, was derived from the expression for the plant radius (eq. 2.24). Predictions of
both z0m and d gives values that are significantly higher than obtained from the profile
methods. Verhoef (1995) suggested that the specification of T| from the assumed plant
shapes and densities might result in values that are too large.
• Discussion of roughness parameter results
The values for z0m found using the profile methods agree very well with the results
reported by Sene (1994) for a similar crop, who found z ^ = 0.01 m early in June, and 0.04-
0.06 m six weeks later. On the other hand, based on the review by Wieringa (1993) the ratio
20m//î = 0.05, found here, is rather low. Kawatani and Meroney (1970) noticed that the
values of d obtained by the regression method of Robinson (1962) and Covey (1963) show a
large variability, and can even become negative. A possible overestimation of d is usually
associated with an underestimation of z0m. Wieringa (1993) lists other possible errors in the
quantification of the roughness parameters:
• the upwind fetch might have been too short, or the terrain might not have been
entirely flat
• the correction for unstable conditions may have been too strong, which gives rise to a
too steep wind profile and too low roughness length
• the lowest sensor (± 1.5 m) might have been too close to the canopy top
• cup anemometer overspeeding particularly occurs near the surface where turbulence
intensity is strong. This also gives too steep wind profiles.
In spite of these uncertainties, values for z0m and d are interpolated from the results
obtained using the profile methods for practical calculations. z0m is given by
day < 15
day > 15 0m
0.01 + 0.01 ^L 15
0.02 + 0.04 ^ 2 1 15
(2.34)
where day is the day in June, 1991. d was kept constant at 0.3 m for further calculations1.
2.4.2 Roughness length for heat The aerodynamic resistance for heat transfer between the surface and a reference
level, ra, can be specified according to
1 De Bruin et al. (1995) assumed that d linearly increased from 0.05 m on 15 June to 0.4 m on 30 June, based on preliminary calculations.
2. Data collection and processing 59
Pc„ T -T
sur a H
(2.35)
where Tsur is an (effective) surface temperature (defined below eq. 2.1), and Ta the
temperature at reference height zR. From eq. 2.35 a so-called roughness length for heat can
be obtained, which can be written as (Blyth and Dolman, 1995):
zR-d
nift exp(r aK«,+«P h((zR-d)/Lj)
(2.36)
in which *Ph is an integrated form of the stability corrections proposed by Dyer and Hicks
(1970; eqs. 2.13 and 2.14). The ratio z0m/zoh can be used to define an additional resistance to
heat transfer, in series with the aerodynamic resistance for momentum transfer applied in
single layer surface models (see section 4.1.1). The quantity 1/K ln(z0m/zofc) is often referred
to as B"1 (Garrat and Hicks, 1973; Kohsiek et al., 1993).
1000ftr
iooo=k
10ft
Figure 2.13: Ratio of z^/zojj as defined using eqs. 2.34 and 2.36. Data shown are derived by using the average (•) and bare soil (») temperature from the low cable. Data of H and u, were obtained from the eddy-correlation device mounted at 4.35 m
0.01 22 23 date (June 1991)
Figure 2.13 shows the ratio z0m/z0h for two different effective surface temperatures,
measured during EFEDA-I: the bare soil temperature as obtained from the low cable, and an
average surface temperature from the same sensor (Appendix II). Around noon, the
difference between these temperatures is typically 4 degrees. Apart from a considerable
scatter of z0m/z0h, its typical value is somewhat higher than values used in SVAT models
presented by Braud et al. (1993), Jacobs (1994) or Viterbo and Beljaars (1995). Furthermore, a
clear diurnal variation is present. Note that Verhoef (1995) reports a considerably lower
value of zoh, by using the single sensor mounted at 4 m height (Table 2.1).
Beljaars and Holtslag (1991) explain that z0m/z0/ j can vary as a result of a vertical
change of the momentum flux to the surface, which is for instance induced by large scale
roughness elements affecting high level wind profiles. Blyth and Dolman (1995) point out
that additional to this aerodynamic effect, zoh for sparse canopies can vary by an order of
magnitude by variations of the distribution of the heat source between the canopy elements
60 Sparse canopy parameterizations for meteorological models
and the underlying soil. More on this issue is discussed in section 5.3, and by Verhoef (1995).
2.4.3 Energy balance terms During the EFEDA-I campaign many methods were applied to measure the energy
balance components. For the model studies reported in later sections a quantitative
assessment of the fluxes of heat, moisture and radiation is of importance.
This section presents some results of the measured fluxes, and discusses the selection
criteria which were adopted to obtain a dataset for further use. Moene (1992) extensively
discussed the methodological differences of various methods, in the context of the
comparability of fluxes measured at different sites with different instrumental set-up's and
methods.
During EFEDA-II surface energy fluxes were determined with eddy-correlation only,
albeit that various sensors were used for the measurement of the latent heat flux (section
2.3.4). In the context of the current work these fluxes were used marginally only for the
examination of the canopy resistance models (section 3.4). Therefore no attention will be
paid to these measurements here.
100 200 300 400 500 600 Q* bare soil (W/m2)
Figure 2.14: Net radiation measured above bare soil and above an individual plant for available half hour averages during EFEDA-I
100 200 300 400 Q* measured (W/m2)
Figure 2.15: Radiation balance from eq. 2.1 plotted against measured net radiation for all available half hour averages during EFEDA-I
• Net radiation In Figure 2.14 the results of the two sensors measuring Q, are intercompared. Shown
are all available half hour averages for 2 -30 June 1991. The value of Q» „;fln( exceeds the bare
soil net radiation by only 1.4% (r2 = 0.996). This difference is rather small, compared to what
is to be expected from differences in the shortwave reflection coefficient of plants (typically
20%) and soil (up to 30%) (Dickinson, 1983). However, the exact position of net radiometers
low above the surface is not a trivial issue. Net radiation measured just above the (darker
and cooler) plants are affected by the surrounding bare soil as well, and do not give a net
radiation equal to a value measured above a homogeneous canopy of the same species. Also
the net radiation measured in between plants will not be representative for the bare soil,
since the large radiometer view angle enables influence of a surface far from the area just
underneath the sensor. These significant mutual effects explain the small differences in the
2. Data collection and processing 61
net radiation values. A 'representative' average net radiation at the field scale was defined
as a simple arithmetic average of the two sensor readings.
In Figure 2.15 net radiation obtained from the radiation balance (eq. 2.1) is compared
to the arithmetic average of the two sensors. For T s u r the average surface temperature as
measured from the high cable and averaged as outlined in Appendix II is used. The surface
albedo, a, was fixed at 0.29 (see section 3.3), and for the surface emissivity a value of 0.98
was taken. The correspondence is good (r2 = 0.990), but an offset of 38 W/m 2 remains. Many
factors may be responsible for this difference. First, sensor calibration errors may be
significant. Also, the assumption that a = 0.29 is uncertain, due to the large variability of the
surface colour and wetness. Finally, the net radiometers mounted at some height integrate
over a different view angle then the radiation thermometer.
• Soil heat flux
The two methods to determine the soil heat flux G during EFEDA-I are compared in
Figure 2.16. Both methods are applied by calculating different soil heat fluxes for shaded
and sunlit plots, and applying a weighted averaging using oy (section 2.2.5). The regression
forced through the origin yields a good correspondence (r2 = 0.933). However, the caloric
method gives lower values for both nighttime and daytime situations. Without clear
evidence for the superiority of either of the methods, we selected the heat fluxes measured
by plates to serve as comparison material for future purposes.
25a
250 G from plates (W/m2)
Figure 2.16: Soil heat flux detected using heat flux plates and by means of the caloric method
• Sensible and latent heat flux
The sensible heat flux data collected during EFEDA-I can be compared to each other in
many ways, due to the many detection methods. De Bruin et al. (1995) compared the values
obtained using the scintillation method to the eddy-correlation data from the low eddy-mast
at 2 = 4.35 m (Table 2.1). They found a fair correspondence, depending on the assumptions
made about the terrain height and the strategy to obtain values of the friction velocity. A
maximal correspondence was found when M» was derived from the same eddy-correlation
62 Sparse canopy pammeterizations for meteorological models
device and the displacement height was allowed to increase gradually from 5 to 40 cm
throughout the measurement period (r2 = 0.956). That result is even slightly better than the
correspondence between the two eddy-correlation sensible heat fluxes from the eddy mast
and the 13 m mast (H{13 m} = 1.02 H{4.35 m}, r2 = 0.951, figure not shown).
Due to instrumental problems, only the eddy-correlation data of the latent heat flux
from the sensor in the 13 m mast were reliable. The remaining eddy-correlation data were
discarded from the present study.
100 200 300 H from 13m-mast (WAn2)
Figure 2.17: Scatterplot of H from the oT method and the eddy-correlation measurements, both from the 13m-mast
150
Î i-i» Q
E 50
Id
-50
• m
• • • ; - • - • - - * /
m
50 100 150 LE from 13m-mast (W/m2)
200
Figure 2.18: As Figure 2.17, but for the latent heat flux
A comparison between the eddy-correlation sensible heat flux and H from the GT
equation from the 13m-mast is shown in Figure 2.17. The coefficients cT1 and cT2 were
specified as 2.9 and 28.4, respectively (De Bruin et al., 1993). The agreement for rather
unstable conditions (Hedd > 50 W/m2) is fair, and a linear regression through the origin
yields HoT = 0.975 Heddy (r2 = 0.938). For Heddy < 0 the o r method gives undefined results,
which is shown clearly in Figure 2.17. A similar plot is given in Figure 2.18 for the latent
heat flux measured using the a equation (eq. 2.9), again using the equipment in the 13m
mast. The agreement is much worse, and the variance method overestimates the eddy-
correlation values significantly. De Bruin et al. (1993) present a likewise low correspondence
using identical equipment operated during the CRAU experiment. They argue that the
method breaks down due to the fact that the correlation coefficient between T and a is
significantly lower than 1. Similar to the large impact of eddies scaling with the boundary
layer height z- on the variance of horizontal wind speed (Van den Hurk and De Bruin, 1995),
the relative contribution from dry downdrafts to the variance of a near the surface may be
rather large. The surface flux is not an appropriate scaling parameter in these cases, and the
applicability of Monin-Obukhov similarity breaks down.
A considerable problem was the determination of latent and sensible heat fluxes
from the profile or Bowen-ratio method. A fair agreement between eddy-correlation and
profile measurements was obtained for the sensible heat flux, but for the latent heat flux the
correspondence was poor (Figure 2.19). In both cases the psychrometers at the lowest level
were not included. Both fluxes are unadequately reproduced when the Bowen-ratio method
is used (Figure 2.20). Again, the lowest measurement level was discarded.
2. Data collection and processing 63
Various combinations of psychrometers (East and West profile, exclusion of extreme
readings) were tried, but in no case the humidity profile was adequate enough to derive
reliable latent heat fluxes from these.
100 200 300 H from eddy-mast (W/m2)
100 200 300 H from eddy-mast (W/m2)
0 50 100 150 LE from 13m-mast (W/m2)
Figure 2.19: Sensible (upper) and latent (lower) heat flux derived from the profile measurements, compared to the eddy-correlation measurements at 4.35 m (H) and at 12.5 m (XE)
50 100 LE from 13m-mast (W/m2)
Figure 2.20: As Figure 2.19, but fluxes derived from the Bowen-ratio method
• Energy balance closure
Based on the presentation of results above the final energy balance that was used for
further intercomparison consisted of:
• an average of the net radiometers from the two low sensors
• the soil heat flux derived from the soil heat flux plates and weighted accordig to oy
• the sensible heat flux obtained from eddy-correlation measurements in the eddy-
mast, at 4.35 m height
• the latent heat flux from eddy-correlation measurements in the 13m mast, at 12.5 m
height.
Figure 2.21 shows the energy balance closure, defined as Q. - H - XE - G, from these
terms for all days during EFEDA-I. The closure is good during nighttime, although a small
64 Sparse canopy parameterizations for meteorological models
but consistent minimum around sunset persists. This is associated to the soil heat flux
correction, which is very large at this time of the day due to a very rapid change of the
surface temperature. The derivation of the change of the heat content of the soil above the
soil heat flux plates may be wrong due to an error in the estimation of the exact temperature
profile near the surface (Appendix II). During daytime generally a surplus of radiative
energy occurred, which peaks to approximately 100 W/m 2 at some days. The hourly
averaged energy balance closure shows a slightly smaller radiative energy surplus (figure
not shown). Especially the low evaporation values recorded during most of the season are
suspected to be erroneous. Also shortcomings in the eddy-correlation method may be
responsible for this disclosure.
20O
12 time (GMT)
Figure 2.21: energy balance closure for EFEDA-I defined as Q, - H - XE - G, where the energy balance components are defined as indicated in the text
2.4.4 Soil thermal properties
In contrast to atmospheric dispersion, transport of heat in the soil involves hardly
any turbulence, and is generally solved using diffusion laws. The model descriptions in
chapter 4 include a treatment of thermal diffusion (section 4.1.2), and a generalized
description of the surface temperature based on diffusion in a homogeneous soil, the force-
restore method (section 4.1.4). These methods make use of the thermal properties of the soil,
in particular the thermal conductivity (kj), diffusivity (fc), and volumetric heat capacity
(P'C„). Verhoef et al. (1995) describe measurements of these quantities from two campaigns
conducted in semi-arid areas: EFEDA-I and HAPEX-Sahel. They discuss the heterogeneity of
these thermal soil properties for a semi-arid sparse canopy surface both in space and in time.
Apart from mesoscale heterogeneity (induced by variable rainfall or crop appearances) the
micro-scale heterogeneity (induced by the partial plant cover) may be important for sparse
canopies, owing to shading and variation in soil moisture content.
In their paper, Verhoef et al. (1995) describe the courses of k and XT for both sunlit
and shaded soil from EFEDA-I, and the bulk volumetric heat capacity (a bulk-value could
2. Data collection and processing 65
only be derived since soil moisture measurements and bulk densities were sampled under
the assumption of a horizontally homogeneous soil). In the current section a summary of
their results is presented.
2.00
Figure 2.22: Volumetric heat capacity obtained from soil bulk density and soil moisture measurements taken in 5 different layers during EFEDA-I
day (June 1991)
Figure 2.22 shows the bulk volumetric heat capacity for 5 different soil layers using
eq. 2.21. Values of the dry bulk density were found to be 1340 kg /m 3 for the top layer, and
1215 ± 25 k g /m 3 for the remaining layers (Droogers et al., 1993). After the last rainfall (0.5
mm on DOY 155; Sene, 1994) maximum values of around 1.6 MJ m"3K_1 were reached in the
layers 0.20 - 0.30 and 0.40 - 0.50 m. The minimum value was about 1.1 MJ m"3K-1. p'Ch
appeared to decrease in all layers as time proceeded, due to a slight reduction of the water
content, co. Values of co ranged from 0.04 - 0.08 m 3 /m 3 for the top layer, and values up to
0.18 m 3 /m 3 were recorded in deeper layers.
The soil thermal conductivity, XT, was obtained directly from the A^needles and
from its definition Xj = k p'Ch. Five methods were applied to derive an estimate of k, of
which the results obtained by the amplitude method, as described in section 2.2.5, are
presented here. The temperature signal from the sensors installed under individual plants
usually showed two maxima, separated by a decreased temperature due to plant shading.
This made the use of the amplitude method for obtaining k for shaded soil parts impossible,
and we confine ourselves to the estimates for sunlit soil.
Values of soil thermal conductivity Xj, derived from the solution of soil thermal
diffusivity using the amplitude equation (eq. 2.19), exhibit a slight variation as time
proceeds (Figure 2.23). In general, Xj increases with depth. In Figure 2.23 the XT values
obtained from temperature readings at depths 25 and 50 cm are discarded, due to large
uncertainties which are involved with the small signal amplitude at these depths. The high
values before 6 June (DOY 157) are a result of the preceding rainfall. The origin of the high
datapoint at 24 June (DOY 175) for A.^3-5 cm) is not clear.
Measurements of XT, carried out at 3 cm depth in both sunlit and shaded soil,
resulted in a nearly constant value of ± 0.10 (sunlit) and ± 0.14 (shaded) W/mK,
respectively. The values at 10 cm depth showed a larger scatter, but were about 0.1 W/mK
66 Sparse canopy parameterizations for meteorological models
higher. The difference between the sunlit and shaded patches is possibly related to a reduction of evaporation by shading. Yet, these measurements are rather low. Ten Berge (1990) shows that minimum values for dry sandy or loamy sand soils exhibit values varying from 0.15 to 0.30 W/mK. Values smaller than 0.10 can be reached, but only for substances containing a very high organic matter content, which was not the case here. A significant underestimation of up to 0.1 W/mK could be caused by poor contact between the probes and the soil, as a result of the loose character (dry conditions) of the soil and the presence of stones in the upper soil layer (Van Haneghem, 1981). Therefore, the suspiciously low measured values of Xj were discarded.
0.7-
0.6-
£0 .5 -
g,0.4-
•% 0.3-3 •a S 80.2-
0.1-
0.0-
m
\\ m
1 ' -rsfs V ^ : ^
1 1 1 1 1
0-3 an
3-5 cm
5-10 cm
10-25 cm
Figure 2.23: Thermal conductivity derived during EFEDA-I from the amplitude equation applied to sunlit soil temperatures at 3 and 5 cm depth, in combination with volumetric heat capacity measurements shown in Figure 2.22
10 15 20 date Qune 1991)
25 30
2. Data collection and processing 67 i
3 Sometimes model equations are presented that make you
wonder whether nature knows them as well
Aerodynamic transfer, albedo, and crop conductance for a sparse canopy surface
3.1 Introduction
A sparse canopy can be defined as a surface whose vegetation does not entirely
occupy the horizontal space. With regard to surface exchange processes, the transfer of
momentum, heat and scalars is governed by both canopy elements and the underlying bare
soil. At a relatively small scale, a sparse canopy is very inhomogeneous. Close to the surface
the vertical fluxes of heat, momentum or scalars will depend on the proximity of individual
canopy elements or obstacles. Horizontal transport between various patches of plants or soil
can be significant. A constant flux layer will not be detectable until far enough above the
surface, where the fluxes of individual surface patches cannot be discerned anymore.
Atmospheric modellers have paid considerable attention to the fluxes of heat, water
vapour and momentum above sparsely vegetated surfaces. Sophisticated surface models
have replaced the simple single layer surface description embedded in the 'big leaf' model.
In these models the surface is treated as a composite of more than just one source, mostly
limited to two (Deardorff, 1978). Various model components (such as aerodynamic transfer
between the source and the atmosphere, radiative properties, and others) are treated for
each source separately. An extensive description of some of these so-called two-layer or two-
component models is given in chapter 4.
In this chapter three aspects which are relevant to the exchange processes for sparse
canopy surfaces are considered:
• aerodynamic transfer
• surface albedo, and
• canopy resistance.
With respect to aerodynamic transfer, we have extended the formulations which are
applied in existing two-layer models using Lagrangian transport theory for closed canopies.
• 68 Sparse canopy parameterizations for meteorological models
We have constructed a new set of aerodynamic exchange resistances, and compared these to
existing resistance formulations for a range of surface types, including sparse canopies. This
theoretical survey is published before by Van den Hurk and McNaughton (1995) and
McNaughton and Van den Hurk (1995), and will be described in section 3.2.
Second, the surface albedo is considered. The variability in time and in space at
various scales will be presented and discussed in section 3.3.
In section 3.4 the canopy resistance for water vapour exchange will be discussed.
Observations taken during EFEDA-II are compared to a canopy resistance model based on
photosynthesis modelling (Jacobs, 1994; Jacobs et al, 1995).
The results presented in this chapter will be summarized in section 3.5. They will
also be included in the one-dimensional simulation study, presented in chapter 6.
Aerodynamic transfer
3.2.1 Concepts based on diffusion theory
At the surface interface, the atmosphere is modified by heating or cooling, water
vapour release or condensation, and scalar exchange. The motion of air is affected by friction
at the surface. The degree of modification of the atmosphere depends on the quantitative
fluxes of temperature, water vapour and momentum.
Similar to the process of molecular diffusion, the surface flux of a constituent x can
be expressed by a gradient of px and a turbulent diffusivity Kx, which is a measure of the
exchange efficiency:
F - -K 3 p * (3.1)
Near the surface, turbulence caused by friction and density gradients is the dominant
exchange mechanism. The exchange efficiency is therefore parameterized as a function of
turbulent fluxes itself.
When over a limited height range the flux doesn't vary significantly with height, eq.
3.1 can be integrated and expressed as a resistance formulation:
F = — (3.2) x r.
where the aerodynamic resistance rx is equivalent to the integrated value of l/Kx over a
fixed height interval, corresponding to the concentration gradient Ap r Within an
atmospheric 'constant flux layer', which is defined as a layer where the vertical gradient of
the flux density of heat, momentum and scalars is insignificant, a resistance formulation is
often used to parameterize H, XE or t. Eqs. 2.13 and 2.14 give expressions for the turbulent
diffusivities as function of the atmospheric stability in a homogeneous surface layer.
In order to derive expressions for the aerodynamic resistances between a vegetated
surface and the atmosphere, assumptions must be made about the concentration- or
windspeed profile in this interval. Calculations of the aerodynamic resistances from an
extrapolation of the logarithmic profile to the top of a canopy result in an overestimation of
3. Aerodynamic transfer, albedo, and crop conductance 6 9 •
rx, owing to extra turbulence generated in wakes behind isolated plant elements (Raupach
and Thorn, 1981). The Simple Biosphere model of Sellers et al. (1986) assumes a logarithmic
profile to be valid well above the canopy top, and includes alternative expressions for
intermediate levels. Furthermore, for sparse canopies also the aerodynamic exchange
between the bare soil surface and the top of the canopy is of importance. Also for this
process several resistance parameterizations have been proposed, based on various
assumptions about the variation of Kx within the canopy. For instance, Shuttleworth and
Wallace (1985) consider an exponential decay of the turbulent diffusivity within the canopy
layer, while Jarvis et al. (1976) adopt a constant diffusivity within a coniferous forest.
Various expressions for resistances within the canopy are included in chapter 4.
In the following sections attention is paid to the physical drawbacks of the concept of
an exchange resistance for describing transfer within canopies. Also a simple procedure is
proposed to deal with these drawbacks.
3.2.2 Implementation of near-field dispersion in a simple two-layer surface resistance model1
Many canopy models have been developed to describe the exchange of sensible and
latent heat between plant canopies and the atmosphere. An important function of these
models is to predict mean profiles of humidity and temperature of the air in the canopy,
because transpiration at each level is controlled by the ambient temperature and humidity at
that level. To calculate these profiles the models must employ some assumption about the
turbulent transport processes in the canopy. The most common assumption has been that
turbulence does transport scalars, such as heat and water vapour, down local concentration
gradients by a 'turbulent diffusion' process. That is, these models have been based on K-
theory (see Waggoner and Reifsnyder, 1968; Shuttleworth and Wallace, 1985; Choudhury
and Monteith, 1988).
In recent years K-theory has been challenged by observations of fluxes of scalars
moving in directions opposed to their local concentration gradients within plant canopies
(Denmead and Bradley, 1985). New theories have been developed which explain counter-
gradient transport, and these show that the diffusivity approach is unreliable under conditi
ons where the vertical length scale of the turbulence is of the same order as the distance over
which the curvature of the concentration profile is significant (Taylor, 1959; Corrsin, 1974;
Raupach, 1988). These new theories have been incorporated into canopy models using a
'higher-order-closure' approach (Wilson and Shaw, 1977; Meyers and Paw U, 1987), and a
Lagrangian framework (Legg and Raupach, 1982; Wilson et al, 1983; Sawford, 1986; Van den
Hurk and Baldocchi, 1990). Unfortunately, such models require detailed information on
canopy structure and consume large amounts of computer time, making them unsuitable for
larger scale hydrological or global climate models. Simple canopy models are more suited to
this application.
Two-layer models designed for sparse canopy surfaces parameterize turbulent
transport within and above the canopy in terms of diffusion resistances. Unfortunately,
these resistances are still derived from X-theory, so the models therefore provide a doubtful
Adapted from Van den Hurk and McNaughton (1995)
70 Sparse canopy parameterizations for meteorological models
framework for calculating scalar exchange within canopies.
Lagrangian models, on the other hand, provide an alternative to JC-theory,
computing concentration and scalar flux density profiles by repeated simulations of a large
number of particle trajectories. Recently, Raupach (1989a) introduced an analytical represen
tation of scalar transport inside canopies based on a Lagrangian description of canopy
transport processes. Being analytic, it requires much less computation time than the
trajectory models.
In Raupach's work the canopy scalar concentration profile is constructed as the sum
of two contributions: one obtained using JC-theory and the other expressing the deviation
from diffusive behaviour. Raupach calls these the 'far-field' and 'near-field' components of
the canopy concentration profile, respectively. Raupach's theory can replace models based
on JC-theory for calculating the microclimate in a multi-layer canopy model, as confirmed by
Dolman and Wallace (1991) and Baldocchi (1992). However, because Raupach's model treats
the canopy as a multi-level source, it still requires a layer-by-layer description of the canopy
turbulence and source strength as input, so it remains unsuited to large-scale applications.
In this section we develop a strategy to implement Lagrangian theory of scalar
transport within a canopy in the practical two-layer resistance model of the canopy energy
balance. We use Raupach's theory to develop an analytical correction to the common two-
layer model. In the next section we explore the difference between Lagrangian and JC-theory
models with respect to the predicted canopy concentration profile. It is shown that in a two-
layer resistance model the calculation of the average concentration in the canopy source
layer can be corrected using a 'near-field' resistance added to the usual resistance network.
This near-field resistor is parameterized using Raupach's analytical Lagrangian theory. A
summary of a strategy to obtain the magnitude of the resistor is given. It will be shown that
it depends on the source distribution and turbulence patterns within the canopy, so we do
not immediately avoid the requirement for a detailed description of the canopy. Therefore,
to see whether individual descriptions of canopies are still necessary, we investigate
whether an assumed 'typical' shape for the source and turbulence profiles can adequately
represent all canopies in Raupach's model. We do this by testing the sensitivity of the
magnitude of the near-field resistor to the shape of these profiles. Details of the Lagrangian
theory, and the implications of including the near-field resistor for evaporation predictions
using a two-layer model, can be found in the original paper (Van den Hurk and
McNaughton, 1995).
• A Lagrangian extension to a two-layer resistance model
Resistance models are usually based on JC-theory, with the aerodynamic 'resistors'
defined by integration of the 'eddy-diffusivity' over the various sections of the diffusion
pathways in the canopy. Integration is possible because the diffusivity has a local value
which expresses the ratio of the flux to the gradient at each level in the canopy. That is, the
local concentration is influenced by the local flux and turbulence only, not by the fluxes or
gradients at other levels in the canopy. However, experimental evidence was provided by
Denmead and Bradley (1985) that much of the turbulent scalar transport within a canopy is
carried out by eddy structures who have a size comparable to the canopy height. This
transport therefore relies on both local gradient diffusion and a larger scale, non-local
3. Aerodynamic transfer, albedo, and crop conductance 7 1 •
contribution. This larger scale contribution is not accounted for by application of first order
K-theory. Lagrangian models, by contrast, take the non-local scalar transport into account,
and show that the concentration gradient at each level depends on the strength of the
sources at all other levels. Lagrangian ideas are therefore incompatible with resistance
models. There is, however, an exception, which we exploit here.
Consider a model of a canopy that has two distinct source layers, an overstorey and
a ground layer. These layers are far enough apart to ensure that the 'non-local' effects which
operate within the overstorey do not influence the concentrations at the ground, and vice
versa. In this case we can therefore describe transfer between the layers, though not within
them, purely in terms of diffusion processes. If we extend the definition of 'resistance' to the
ratio of concentration difference to flux, without the requirement that this ratio is well
defined at all points along the integration path between the layers, then we can describe the
transport between these layers in terms of a 'vertical' resistance, and the resistors can play
the same formal role as the aerodynamic resistors in, for example, the two-layer model of
Shuttleworth and Wallace (1985).
This does not solve all of our problems. The 'vertical' resistances that will give the
correct transport between the separate layers, being the ground, overstorey and reference
height, will not give the correct concentration within the overstorey canopy. In K-theory
models the strong local concentration gradients near sources cause rapid dispersal of the
scalar. In Lagrangian models this is much less marked because scalar movement depends
solely on the statistics of the turbulence and not on diffusion over the local concentration
gradient. As a result Lagrangian models predict higher concentrations near sources than do
jK-theory models. The origin of the difference between the predicted concentration near the
source is the non-local transport of scalar emitted by sources in the entire source range,
which is parameterized in Lagrangian models and not in K-theory models. Since this
concentration rise is not predicted by diffusion theory we call it a 'non-diffusive'
contribution to the scalar concentration.
Figure 3.1: Resistance network of a two-layer surface model. The source and corresponding concentration values of only a single scalar source are considered. Flux densities are regulated by appropriate concentration gradients and resistances. Also, the near-field resistance rn is implemented in the pathway of the canopy source (for further explanation see text; Cb will be introduced in section 3.2.3)
A possible strategy to account for this non-diffusive concentration rise within the
overstorey is to add a 'lateral' resistor in the resistance network, which will isolate the
canopy from the vertical diffusion components. The arguments for doing this and the
72 Sparse canopy parameterizations for meteorological models
quantification of the magnitude of the resistor are based on the 'Localized Near-Field'
theory of Raupach (1989a). We note that the resistance network now departs from the usual
forms by having a virtual node where the vertical and lateral resistors join. The new
resistance configuration is shown in Figure 3.1.
In Figure 3.1 the total scalar flux from the surface to the atmosphere, Ft, consists of a
contribution from the soil or ground vegetation, Fs, and a flux from the canopy layer, Fn. The
resistances rac and rf describe transport from the canopy leaves to the air surrounding them,
and represent the bulk boundary-layer and bulk stomatal resistance, respectively. Two
resistors, ra" and ras, describe diffusive transport from the canopy to a reference level above
the canopy and from the ground to the canopy. The concentration at the virtual node, Cv is
the concentration resulting from diffusive transport through ra" and ras. The extra resistance,
labelled rn, is included to allow a higher concentration, Cc, to build-up because of non-
diffusive transport near the source in the overstorey. Cc is an observable concentration
value, whereas Cv is observable only when non-diffusive transport is absent.
With this configuration it is possible for the flux through ras to be directed upwards
even when the concentration Cc is higher than that at the ground, Cs. That is, this
configuration allows observable counter-gradient transport within the lower canopy, even
though the fluxes through all the resistors are well-behaved and flow down the
concentration gradients. This situation is shown in Figure 3.2. Similarly, a counter-gradient
transport above the canopy is allowed according to the scheme in Figure 3.2. Here the
reference concentration CR is smaller than Cc, but a net downward transport is simulated.
Figure 3.2: Influence of rn on average concentration represented by the scheme of Figure 3.1. Continuous lines indicate flows according to Figure 3.1, whereas dotted lines represent apparent concentration gradients. The arrows indicate a region of a simulated flux density against the gradient of C. (A) Counter-gradient transport within the canopy; (B) Counter-gradient transport above the canopy
This new model is in a good form to accomplish our purpose since it is no more
difficult to implement than existing two-layer resistance models. Just like traditional two-
layer models, the vertical concentration profile consists of a reference concentration, a
concentration value at the ground surface, and an averaged value of the concentration in the
overstorey. The model gives a physically improved value of the average overstorey
concentration when the non-local contribution to scalar transport is parameterized by the
resistor rn. The remaining, crucial step is to evaluate the value of rn. For this we use the
'Localized Near-Field' (LNF) theory of Raupach (1989a). Details of this theory are given by
Van den Hurk and McNaughton (1995). The next section gives a brief description of the
3. Aerodynamic transfer, albedo, and crop conductance 73
strategy to obtain rn.
• Parameterization of rn using Raupach's 'Localized Near-Field' model of scalar transport in a plant canopy
Raupach's LNF-theory gives an analytical description of a canopy concentration
profile, C(z). For reasons outlined by Van den Hurk and McNaughton (1995), Raupach
distinguishes two contributions to C(z): the near-field and far-field components. The far-field
concentration profile obeys diffusion theory, and can thus be modelled by a multi-layer
resistance model like that of Waggoner and Reifsnyder (1968). The origin of the near-field
concentration, Cn(z), is non-local: it is determined by the source strength in neighbouring
layers. Therefore, Cn(z) can not be represented in terms of a resistance model. The values of
the resistors would have to depend on the source strength at neighbouring levels.
However, in a larger-scale application we will not require detailed information on
the concentration profile within the canopy. Therefore, it will be sufficient to find a
successful expression for a representative average value of the near-field concentration, C„.
This average near-field concentration can be related to the scalar flux density originating
from the canopy source Fh using a resistance formulation:
(3.3)
h
The near-field resistance rn expresses the average concentration rise in a source layer per unit
canopy flux due to near-field effects. To implement rn in a common resistance model it is
required that the scalar transport between the distinguished source layers is diffusive. In
other words, the near-field contribution to the scalar concentration in any source layer must
originate from that source layer only, and no overlap of near-field contributions from other
source layers is allowed. We emphasize that for a two-layer resistance model such a
representation is possible only when the whole overstorey is combined into a single layer,
and the underlying ground source does not exhibit near-field transport effects. The
resistance network then is outlined in Figure 3.1. In multi-layer resistance models the layers
must be spaced wide enough to avoid overlap of near-field contributions. Raupach's
original methods are appropriate for more complex models.
Two issues must be solved before Cn and thus rn can be found. First, the definition of
a 'representative average' Cn must be specified before it can be computed from the profile of
Cn{z). A weighing function is used for this purpose, and this is discussed hereafter. Second,
prediction of the near-field concentration profile requires that we provide a description of
the vertical distribution of canopy sources, S(z), and turbulence within the canopy,
characterized by the standard deviation of the vertical wind speed, csw(z), and a Lagrangian
time sclae, T^z). Usually we will not have a detailed knowledge of these distributions.
Therefore, we will investigate whether a standardized description of a typical canopy source
distribution and turbulence profile can give a value for the average near-field concentration
within the overstorey adequately representing all relevant canopies.
74 Sparse canopy parameterizations for meteorological models
• Averaging the near-field concentration
The average near-field concentration, Cn, can be calculated in several ways,
depending on what is required. Our problem here is to predict the total evaporative flux
from the overstorey. This leads us to focus on obtaining the correct average of the saturation
deficit D within the overstorey, since the evaporation rate from each leaf is driven by the
saturation deficit of the canopy air at that level, D0. At each level in the canopy the
Penman-Monteith equation dictates that the 'effectiveness' of D0 depends on the leaf area
density divided by (A + y)rb + yrst, where A is the change of saturated water vapour
pressure with changing temperature, y the psychrometer constant, and rb and r$t represent
leaf boundary layer and leaf stomatal resistance, equivalent to the resistors as given in
Figure 3.1 (Monteith, 1973; McNaughton and Van den Hurk, 1995). For this reason it is more
important that D0 is accurate at levels with large leaf area density and small resistances. In
forming an effective average of D0 the values at each level should be weighted to reflect this.
Unfortunately we cannot assume that profiles of leaf area density, stomatal resistance or leaf
boundary-layer resistance are known, so we use the source distribution S(z) itself to
represent the weighing function. The source distribution is already needed to obtain Cn(z)
(see Van den Hurk and McNaughton, 1995), so this implies no new data requirement. We
recall that eventually S(z) is to be replaced by a standardized profile, and the uncertainty
with respect to energy balance calculations of this strategy is discussed later.
The average near-field concentration over the depth of the overstorey, Cn, can now
be calculated as the weighted average of the profile of Cn:
(3.4) Cn
/•(2)C„(z)dz h
= ° = f<Kz)C„(2)dz r ° J4>(z)dz 0
Here, <t>(z) is a normalized source distribution function, defined as S(z)/Fh. <|)(z) is zero
below and above the canopy source range and integrates to unity over the source range
height. rn has dimensions of time/length, so multiplying it by the friction velocity «» gives a
non-dimensional transfer resistance similar in function to the inverse of the drag coefficient
often used in momentum calculations. We will identify this quantity, u, Cn/Fh (= u» rn), by
the symbol 5Rn and report the results of all our calculations as values of 95n. This has the
advantage that the reported results are independent of wind speed. To evaluate 5Rn we must
know the profiles of ow, T; and (|). These profiles will be explored next.
• Sensitivity analysis
(a) The profiles ofcw(z), Tj(z) and ty(z)
The near-field concentration profile Cn(z), and thus its weighted value 9în are
determined by the profiles of the turbulence parameters, aw and T;. Raupach (1988) argues
that the empirical data available justify the formulations
3. Aerodynamic transfer, albedo, and crop conductance 7 5
«„<*> z/h>\ (3.5a)
CQ + (Cj - c0) z / / i z / /z < 1
T ; ( Z K . K ( z - d ) . M B _ . = max[c 2 ,_ l_—1] (3.5b)
where h is the canopy height, and d is the displacement height, h and u» are considered as
the governing scaling parameters and assumed known. The coefficients are quantified as
c0 = 0.25, c1 « 1.25 and c2 = 0.30. By eqs. 3.5 the eddy-diffusivity K = ow2 Tt approaches the
limit K u» (z - d) predicted by Monin-Obukhov similarity theory well above the canopy
(Raupach, 1988). These relationships are based on both wind tunnel and field observations,
but none of them are from very sparse canopies where a significant fraction of the total
momentum flux to the canopy is dissipated at the ground. The exact nature of the canopy
turbulence is only partially covered by the simplified parameterization of aw. The
significance of this uncertainty for the average near-field concentration will be examined
below by performing calculations with various choices of the parameter c0, the value of
ow/u* at the ground. The Lagrangian time scale T; inside the canopy is assumed to be
uniform with height. There is little reliable information on the variation of this quantity
among different canopies so this assumption will not be explored here.
The remaining profile, <|>(z), depends on both physiological and physical properties
of the canopy, as explained above. A common procedure to estimate <|>(z) is to assume that it
is proportional to the product of net radiation and leaf area density at level z. However,
since we cannot assume a detailed knowledge of any of these, our strategy is to explore a
range of <|>(z) functions, constructed so as to encompass the source distributions found in a
wide range of canopies. To do this we utilize the Beta-distribution and the block-function.
These functions are illustrated in Figure 3.3. The Beta-distribution (see eq. 8 in Appendix III)
has earlier been used to represent profiles of leaf area density (e.g. Meyers and Paw U,
1986). It resembles the well-known Poisson-distribution but integrates to unity in the range
0 < z/h < 1. Two parameters, p and q, determine the shape of the distribution. When p > q,
the maximum value occurs where z/h > 0.5, so this represents a source which is
concentrated in the upper part of the canopy. For dense, horizontally homogeneous
vegetation stands, the source profile of water vapour and heat will tend to resemble the
absorption profile of net radiation in the canopy. For crops having leaves over the entire
canopy depth, like most agricultural crops, the source profile is therefore represented best
by a Beta-distribution where p > q. Measured profiles of the daytime water vapour flux
density in bulrush millet measured by Begg et al. (1964) were rather well fitted by a Beta-
distribution with p = 4 and q = 2. Similar profiles in a maize stand described by Brown and
Covey (1966) were well reproduced by using p = 3 and q = 2. Forest stands usually have
leaves in a limited height range high in the canopy, and therefore generally show a source
profile which is more concentrated near the canopy top. A Beta-distribution with p = 6 and
• 76 Sparse canopy parameterizations for meteorological models
q = 2 gave a good simulation of the measured latent heat flux profile in the deciduous forest
stand of Denmead and Bradley (1985), whereas a distribution with p = 4 and q = 2 provided
a good fit to the latent heat flux profile measured by Droppo and Hamilton (1973) in a
similar stand rather well. Some examples are shown in Figure 3.3a.
The block-function spreads the source uniformly over the upper n% of the canopy, as
shown in Figure 3.3b. Corresponding block functions representing sources near the ground
surface are not considered, because the definition of the canopy height h becomes
questionable when the canopy source does not extend to the top. In all cases !0h ty(z) dz
equals 1, as required by our definition of <|>.
LOOre
•g 0.50
3.00
0.75
0.50-
0.25
000 z
z = [0.6,1]
z = [0.2,1]
= [0,1 B 3.00 1.00 2.00 3.00
Figure 3.3: Examples of source profiles. (A) Beta distributions with (p, q) parameters as indicated; (B) block function with source concentrated in relative height ranges as indicated
(b) Sensitivity of the average near-field concentration to ty(z) and om(z)
Values of 9în have been computed using eq. 3.3 with a representative range of source
and turbulence profiles. The source profiles, <Kz), were generated by selecting suitable
values of the parameters p and q for the Beta-distribution or source thicknesses for the block
function, as described above. The turbulence profiles were generated by selecting a suitable
range of values of the parameter c0 in eq. 3.5a. A value of 0.25 is cited by Raupach (1988)
and others as a likely value for most canopies. Here the calculations are extended to
0.25 ± 0.25. c0 = 1.25 is added to include the widest extreme, in which case no gradient of ow
within the canopy is present. The parameters c1 and c2 were set to 1.25 and 0.3, respectively.
Results from these calculations are listed in Table 3.1.
The calculated results show that 5Rn is not very sensitive to the selected value of c0,
and hence aw(z). The sensitivity to the form chosen for the source profile <|>(z) is somewhat
larger. The values of 3in range from 0.26 to 0.46 for almost all plausible canopy
representations, and from 0.32 to 0.40 for the most likely cases. Only where a very thin
canopy layer is situated far from the ground (represented by the block function [0.8,1]) does
9ln take a higher value.
This conservative behaviour of 9t„ can be explained as follows. A source contributes
to the near-field concentration mainly at levels quite near that source. About 80% of the total
near-field effect is felt within the distance given by öwT;, which is less than 37% of the height
of the canopy at all levels in the canopy source range, according to eq. 3.5. Therefore, Cn will
be largest when the source is highly concentrated and smallest when it is widely distributed.
3. Aerodynamic transfer, albedo, and crop conductance 77
Table 3.1: Values of 9în = rn u. as function of various profiles of <|>(z) and aw(z). The profile of aw/u. linearly increases from c0 at z = 0 to c1 = 1.25 at z/h = 1. The source profile <|>(z) of type Beta-distribution is changed by adopting various values for the parameters p and c\. zrmx is the level where (|>(z) is maximum (see Figure 3.3a). The source profile represented by the block function is changed by adjusting the lowest boundary of the source range, and keeping the highest boundary fixed at z/h = 1 (Figure 3.3b)
Source type: Beta-distribution
parameters (p, q) z„„r/h
2,4 0.25
2 , 2 0.50
4 ,2 0.75
6 ,2 0.83
Source type: block function
range {z/h)
0.0 - 1.0
0.2 - 1.0
0.4 - 1.0
0.6 - 1.0
0.8 - 1.0
c„=0.0
0.43
0.32
0.36
0.41
0.26
0.31
0.37
0.46
0.63
c„=0.25
0.42
0.31
0.36
0.41
0.27
0.30
0.36
0.45
0.62
c„=0.50
0.41
0.31
0.35
0.40
0.27
0.30
0.35
0.44
0.61
cn=1.25
0.38
0.30
0.33
0.38
0.26
0.28
0.33
0.42
0.59
Thus the narrowest canopy source, described by the block distribution [0.8,1] gives the
largest resistance, and that described by the block distribution [0,1] gives the lowest value.
Along with this effect is the tendency of turbulence to spread the near-field concentration
from a source beyond the bounds of the canopy, and so beyond the range of integration.
This will tend to reduce 9?n for larger values of ow. We see very little effect of increasing c0
(which increases ow at all levels within the canopy) for well-distributed sources such as the
block distribution [0,1], but a noticeable decrease in 5Rn with increasing ow for more
concentrated sources.
An average near-field concentration 9?n can be deduced from Table 3.1, concentrating
on the likely values of p and q cited above. This results in a value of 0.36 ± 0.05 for most
dense crops. Vegetation stands with a more open structure will distribute the net radiation
more equally over the entire canopy depth, and the average near-field concentration will be
somewhat lower in these cases.
Van den Hurk and McNaughton (1995) evaluated the effect of including rn = 0.36/M»
in the two-layer resistance model of Shuttleworth and Wallace (1985). They performed
calculations representative for conditions of calm wind and clear sky, for various watering
conditions, determined by the choice for the crop resistance and soil evaporation resistance.
They concluded that for both dense crops (LAI = 4) and sparse crops (LAI = 1) including rn
makes very little difference to the energy balance of the canopy and the ground. The largest
effect is present when all other resistances in the model (see Figure 3.1) are low.
78 Sparse canopy parameterizations for meteorological models
• Conclusions
It is possible to represent non-diffusive transport in canopies in a two-layer
resistance model, such as that of Shuttleworth and Wallace (1985), by adding a 'near-field'
resistor, rn, in series with the bulk boundary-layer resistance in the upper layer of the model.
Addition of this resistor has an improved prediction of the scalar concentration in the
canopy source layer as a diagnostic, and allows the model to mimic the counter-gradient
transport of scalars that is sometimes observed within real canopies. The procedure of
adding a near-field resistor into the upper layer can only be applied when the near-field
contributions from the separate source layers do not overlap.
The value of the normalized near-field resistor can be calculated using the analytical
Lagrangian model of canopy transport developed by Raupach (1989a). The calculated values
of 9în = rn u, range from 0.26 to 0.63, with the likely value for most canopies described by
0.36 ± 0.05. The higher values in this range are for canopies where the leaf area is
concentrated in a narrow range, while the lower values are for canopies with
well-distributed leaf areas. The values of rn are rather insensitive to how the turbulence
(expressed in terms of ow) is described within the canopy, and moderately sensitive to the
shape of the source profile.
Addition of this near-field resistance into the Shuttleworth and Wallace model has
only a small effect on the predicted evaporation rate from both the canopy and the
underlying soil, under calm wind and clear sky conditions. This is because rn is less than
one tenth the magnitude of either of the aerodynamic resistances included in the
Shuttleworth and Wallace model. The overall minor influence on the surface evaporation
justifies the crude estimation of rn given above.
In this study the physiological response of leaves to the ambient water vapour deficit
is not taken into account. The canopy resistance is explicitely specified and not made
dependent on the canopy water vapour deficit. Since rn affects the average concentration
within the overstorey a possible extra effect via rsc might take place. Under conditions of
strong canopy evaporation the effect of rn will be to reduce the canopy water vapour deficit,
thereby possibly also reducing rsc and counteracting the (slight) reduction of the canopy
evaporation. The opposite takes place when sensible heat flux dominates the canopy
evaporation. Further examination of a system where these feedback mechanisms are
included requires a description of the response of rsc to changing canopy water vapour
deficit, and is a possible item for future research.
Theoretically, rn could also be evaluated using other sophisticated theories such as
higher-order-closure. The improved prediction of within canopy concentration profiles
compared to first-order closure (Meyers and Paw U, 1987) makes this excercise certainly
worthwile. An experimental evaluation of rn will encounter major difficulties in defining
effective averages of the relevant resistances (including rn) and in measuring the canopy
source and turbulence profiles.
The small value of rn is somewhat surprising, given the weight of the objections
against using X-theory for the description of canopy transport processes. Simultaneously it
gives also rise to questioning the need to implement near-field effects in larger scale models.
The present study shows that for a correct prediction of energy fluxes from relatively
complex surfaces much emphasis must be laid on a correct parameterization of the other
3. Aerodynamic transfer, albedo, and crop conductance 79 •
aerodynamic and physiological resistances. A theoretical discussion of raa, ra
s and rac is
presented in the next section.
3.2.3 A 'Lagrangian' revision of the resistors in the two-layer model for calculating the energy budget of a plant canopy2
In the previous sections (Van den Hurk and McNaughton, 1995) it was shown that
Raupach's 'Linearized Near-Field' theory (Raupach, 1989a) can be used to construct a two-
layer resistance model. This new model has the same structure as earlier two-layer models,
except that a 'near-field resistor' is placed in series with the boundary-layer resistor. The
other resistors of the two-layer model were not discussed. McNaughton and Van den Hurk
(1995) completed this revision of the two-layer models by re-evaluating them, again basing
calculations on the Lagrangian LNF-model of Raupach (1989a,b). Using Raupach's concepts
they replaced the aerodynamic resistors of e.g. Shuttleworth and Wallace (1985) with 'far-
field' resistors, and quantified them using Raupach's expression for the 'far-field' diffusivity
(Raupach, 1988). The same was done with the boundary-layer resistance of the foliage in the
overstorey canopy. The result is a completely-reformulated two-layer resistance model.
In the following sections the derivation of the newly defined far-field resistors is
summarized. Calculated values of (normalized) far-field and boundary-layer resistances are
compared with those of Shuttleworth and Wallace (1985) and Choudhury and Monteith
(1988). McNaughton and Van den Hurk (1995) also compared the resistors from these two-
layer models to experimental values found in the literature, expressed in terms of the
'excess' resistance. This experimental comparison is not repeated in this thesis.
• The Far-Field resistors
In the previous sections Van den Hurk and McNaughton defined a near-field resistor
as the ratio of an effective average near-field concentration, Cn, to the canopy flux (eq. 3.3).
Cn is defined as the single value of Cn whose inclusion in the two-layer model would have
the same effect on the energy fluxes as inclusion of the true profile, Cn(z), has in the full
model. This average concentration was found by integrating Raupach's profile equations
and applying a weighing function (eq. 3.4). McNaughton and Van den Hurk (1995), referred
to as MH95 hereafter, continued to use effective concentration values to define the remaining
resistors in their model.
Because the far-field profile in Raupach's LNF theory is described by K-theory,
vertical diffusion within and just above a canopy can be represented by a vertical chain of
resistors. In a two-layer model only two layers are present, so this chain has only two
resistors: an 'upper far-field resistor' and a 'lower far-field resistor', labelled ra" and ras in
Figure 3.1.
Their methods for evaluating the resistors from the K-profile differ from those used
by Shuttleworth and Wallace (1985) and Choudhury and Monteith (1988). MH95 based their
calculations on complete integrations over the far-field concentration profile, CÂz), without
first reducing the source profile to a single source at a specified level. This avoids any ad hoc
specification of 'the source level' and allows to discuss the effect that the shape of the source
2 Adapted from McNaughton and Van den Hurk (1995)
80 Sparse canopy parameterizations for meteorological models
profile has on the calculated resistances.
The Upper Far-Field Resistor
Referring to Figure 3.1, the upper far-field resistor, ra", is defined by the equation
CV-CR (3.6)
where the concentration at the reference level, CR, and the total scalar flux upwards at the
reference level, Ft, are observable quantities. Cv is the effective weighted average of the far-
field concentration within the overstorey, given by
C „ - ƒ<> (çJC/ç) dç (3.7)
where Cris the solution of the diffusion equation (see McNaughton and Van den Hurk,
1995), ç = z/h, and <|)(ç) is the same weighing function as outlined above. This leads, with
eq. 3.6 and a little manipulation, to an expression for the dimensionless upper far-field
resistor:
ƒ•<«> 'V
hu
K(q) Vdç' dç
(3.8)
The expression on the right can be expanded by splitting the innermost integral into
integrals from ç to 1 and from 1 to çR. Some further manipulation then leads to the
dimensionless equation
ÇR hu. hu. ur" = f Idç + U(q) f Ldç/dç
(3.9) 1 hu. '
•t o
Eq. 3.9 has three terms on the right. The first, 9îj (where 91 denotes a dimensionless
resistance, equal to r u,), represents the part of the far-field resistor above the top of the
canopy. The second, 9lw, represents the far-field resistance up to canopy top calculated as if
the whole canopy source were located at the bottom of the canopy, but with the
effectiveness weighing distributed through the canopy. The third term, (f^/Ff)^/;/, is a
correction for the true distribution of sources. The ratio Fh/Ft lies in the range 0 - 1 . This
third term will be different for each canopy so its presence signals the impossibility of
constructing a perfect two-layer model with resistors independent of the source distribution.
Table 3.2 lists values of 9îj, 9l77 and 5Km for various profile shapes of ow (modified by
ranging c0 in eq. 3.5) and <|> (parameterized as a Beta-function, as before). çR is set at 2
3. Aerodynamic transfer, albedo, and crop conductance 81
Table 3.2: Components of the dimensionless far-field resistor calculated for three values of c0 and a range of assumed source distributions, <Kç), described by Beta-probability distributions with the p and q values shown (see also Figure 3.3a). 95p 1HU and %m are the three integrals in the respective terms on the right of eq. 3.9. 95, is computed by using çR = 2 and d/h = 0.66. The upper far-field resistor, 9!/, is calculated assuming Fh/Ft = 0.5, so that 91/ = 9t, + 9t„ - 0.5 9t,„. 9tw is the dimensionless resistor defined by eq. 3.12 and 3.15, and 9Ja
s is the dimensionless lower far-field resistor, also for F/./F, = 0.5, so that 9tas = 9î,v - 9t„ + 1 9ira
<=n
0.15
0.25
0.35
P
1.25
1
2
3
6
1.25
1
2
3
6
1.25
1
2
3
6
1
2
1
2
2
2
2
1
2
2
2
2
1
2
2
2
», 2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
2.1
S i ,
4.3
3.4
2.7
1.7
0.8
3.4
2.7
2.3
1.5
0.7
2.9
2.3
2.0
1.4
0.7
*m
1.9
1.9
1.2
0.8
0.3
1.4
1.4
0.9
0.6
0.3
1.0
1.1
0.8
0.6
0.3
V 5.5
4.6
4.2
3.4
2.8
4.9
4.1
3.9
3.3
2.7
4.5
3.9
3.8
3.3
2.7
%v
17.8
17.8
17.8
17.8
17.8
10.7
10.7
10.7
10.7
10.7
7.6
7.6
7.6
7.6
7.6
V 15.4
16.3
16.4
16.9
17.3
8.6
9.4
9.3
9.8
10.2
5.8
6.4
6.4
6.8
7.1
(above this level the scalar profile should be well described by the usual Monin-Obukhov
similarity forms, so resistance from that level up to any other level can be calculated in the
conventional way), and d/h = 0.66 is assumed.
The above-canopy part of the far-field resistance, 5Rj, is the same for all cases, but the
resistances within the canopy are somewhat sensitive to the shape of the ow profile, as
specified by c0, and very sensitive to the assumed source distribution. The values of 5RW and
5RWj for a source concentrated near the top of the canopy are only about one fifth of those for
a source concentrated near the bottom. The values of SRflfl can be roughly estimated by
rewriting eq. 3.9 as
K-^^n-^iu (310)
and setting Fh/Ft to a mid value of 0.5. These values are also shown. An SRafl-value of 3.6 ±
1.0 is appropriate for most canopies. This gives the dimensioned value of the upper far-field
resistor as ra" = 3.6/u», where the value of M» is assumed known.
The Lower Far-Field Resistor
As with the upper far-field resistor, the lower far-field resistor was defined as to
• 82 Sparse canopy parameterizations for meteorological models
preserve correctly a particular quantity: in this case the concentration at the ground, Cs.
Referring to Figure 3.1, the lower far-field resistor, ras, is defined by the equation
(3.11)
where Cs is found by integrating down the concentration gradient, Ciz), from the reference
height right down to the ground. Substituting for Cv using eq. 3.7 leads to the dimensionless
equation
9C-«. (C 8 -CR ) 9 f o ( 3 1 2 )
Fs
where (Cs - CR) is found by extrapolating the far-field concentration profile down to the
ground at q = 0, so that
U>{C°-CR) -1 ^Ldç.+FJL1 ^L k w d ç <3 1 3>
Fs l m Fsimr^' The first integral here may be split into integrals from 0 to 1 and from 1 to qR. The integral
from 0 to 1 we designate 9t/v, while that from 1 to çR is already designated 5Rj. The second
integral term in eq. 3.13 is just Fft/Fs(9tj + SRn). With these substitutions eq. 3.13 becomes
" , ( C S - C R )
Substitution of eq. 3.10 into 3.14 leads to
' F ^
l+lÜ F„
h *i^*u + *iv ( 3-1 4 )
F < = *iv-*ii + -f*m a i 5 )
Calculated values of 3ijV are shown in Table 3.2, using Fh/Fs = 1 as before.
Table 3.2 shows that, for a given value of c0,5Rfls varies less than about 20% over the
full range of assumed overstorey source distributions when Fh/Fs = 1.0. On the other hand,
the table shows that SRfls varies by a factor of 2.5 as c0 ranges from 0.15 to 0.35. Even this
range of c0 may not express the true uncertainty because the profile equation 3.5 becomes
unreliable as the ground is approached. This is just where the diffusivity is smallest and
makes the largest contribution to 91/ , so the value 9tas is, in fact, highly uncertain. Similar
uncertainty exists in other two-layer models for the same reason.
From Table 3.2 we choose 5R/ = 10 as a representative value, so that ras = 10/u».
The Boundary-Layer Resistance
MH95 defined the dimensionless boundary layer resistance, 9tb, to be the one that
satisfies the relationship
3. Aerodynamic transfer, albedo, and crop conductance 8 3 I
9L = ' b c (3.16) b p
th
Here, Cc is the canopy airstream concentration (Figure 3.1), and (Cb - Cc) is the effective
increment of concentration given by an equation similar to eq. 3.4. The concentration
difference across the boundary-layer resistances at each level in the canopy is given by
C ( ç ) - C ( ç ) . ^ î f ^ (3.17) b(q' c(q' MD(ç)
where Sh is the total canopy source strength. This leads to
*> -"• /r»(s)T35Grdç " m ( ç ) dç (3-18)
o LAD(ç,) LAI •
where an effectiveness weighing, (p(ç), was eliminated by (crudely) assuming that its profile
resembles the profile of L4D(ç).
The leaf boundary-layer resistance, rfc(ç), depends on leaf dimension, lw, wind speed,
u(ç) and other factors such as leaf shape and degree of mutual sheltering of the foliage and
the intensity and scale of turbulence. If we model the leaf as a flat plate parallel to the flow,
then heat transfer from both sides is given by (Appendix III)
150 ß lw (3.19)
N u
where the sheltering factor ßs was assumed to be 1. The wind speed, u, was expressed using
an exponential decay function with attenuation coefficient au (Cionco, 1972,1978; Pereira
and Shaw, 1980). Furthermore, MH95 assumed that, in cases where the canopy is dense
enough that very little momentum is transferred to the ground, the ratio uh/u, = 3.2
(Raupach, 1992). This leads to an expression for the dimensionless boundary-layer resistance
of the overstorey canopy, written as
F i — * *b = 8 4 -^ rJ" e x p - r ( 1" ç ) 4>fe)dç
V -0
/
(3.20)
from which ^LAI/J^u^ can be evaluated directly using an appropriate range of au-values
to represent a range of wind profiles, and the Beta function to represent a range of source
profiles. The results of the calculations are shown in Table 3.3.
In Table 3.3 the small values of au represent sparser canopies, where we might
expect good radiation penetration and the flux sources to be spread more evenly or
concentrated low in the canopy. Larger values of au, on the other hand, represent denser
canopies, where flux sources would often be concentrated higher in the canopy (Cionco,
1978; Pereira and Shaw, 1980). The p and q parameter values in Table 3.3 reflect, from left to
right, a similar trend towards higher sources. The most representative values from Table 3.3
• 8 4 Sparse canopy parameterizations for meteorological models
Table 3.3: Values of 9?6LA7/i/"i!1,H„ in s1/2m_1, calculated using eq. 3.20 for various values of the attenuation coefficient for the canopy wind profile, au, and the source distribution function (|)(ç) represented by the Beta-function with values of the parameters p and q as shown. The devalues 1, 2, 3 and 4 correspond to leaf area indices of about 0.6, 2, 4 and 9, respectively, depending on canopy structure, according to calculations by Pereira and Shaw (1980)
wind profile
<xu = l
«„ = 2
<x„ = 3
«„ = 4
p = 1.25 9 = 2
115
160
224
319
p = l q = l
109
144
195
268
p = 2 q = 2
109
142
188
252
p = 3 q = 2
103
128
160
203
p = 6
1 = 2
95
109
125
145
should therefore lie about the diagonal through the table from upper left to lower right. Wind profiles in most crops are described by au values between 1.3 and 2.8; higher values of au are observed in many forests. A representative value of 3ibLAI/Jlwut from Table 3.3 is about 130 s1 '2!^1 with most canopies probably within ± 30 s1'2!«"1 of this figure. Unlike SRfl
fl, 3îfl
s and 9?n, which take fixed values, 5Rfc depends on the momentum flux to the canopy and on the canopy leaf area index and leaf dimension. Values of SRj, can vary over two orders of magnitude, depending on the values of these parameters, so some direct information about the canopy is needed. An estimated dimensional value of the bulk boundary-layer resistance, ra
c, is therefore 9tb/u» = 130/LAlJlw/ut .
• Comparisons with resistors of other two-layer models MH95 compared the values of the resistors in their re-evaluated two-layer canopy
model with formulations presented by Shuttleworth and Wallace (1985; SW85) and Choudhury and Monteith (1988, CM88). The CM88 model differs from the original SW85 model in two principal ways: a better treatment of leaf boundary-layer resistances, and modifications which allow a continuous transition from canopies with dense overstoreys to canopies without overstoreys. The model of MH95 was not intended for use with very sparse overstoreys, so the comparison was restricted to canopies with overstoreys that are dense enough that very little momentum reaches the ground.
Table 3.4: Intercomparison of dimensionless resistances; 9?„ is the near-field resistance, 91," the upper far-field (or aerodynamic) resistance, 9tn
s the lower far-field (or within canopy aerodynamic) resistance, and 9tj, the leaf boundary-layer resistance
quantity SW85 CM88 MH95
»/ 95/
%LA1/S(lwu,)
0
5.5
28
0
5.4 - 6.7
15 -60
7 5 - 9 7
0.30 - 0.42
2.6 - 4.6
6 - 1 7
100 - 160
Table 3.4 gives a summary of the dimensionless resistors. In each case the reference height is set at 2h, and stability corrections are ignored.
3. Aerodynamic transfer, albedo, and crop conductance 85
Both SW85 and CM88 calculate 9?a" and 5R/ by integrating the inverse of a diffusivity
function, equal to K(q)/uM = K(Ç - d/h) above the canopy, and K(l)exp{n(ç -1)} below ç = 1.
n is an eddy-diffusivity extinction coefficient, set to 2. 9?flfl is found from an integration from
a source level at height (z0m + d) up to the reference height. SR/ is integrated between the
source height to a level near the ground, z0'. The value of z0 ' has almost no effect on the
calculation. The principal difference between the models is how z0 and d are calculated.
SW85 assumes z0m//z = 0.13 and d/h = 0.63, which values are typical of agricultural crops.
CM88 lets züm and d depend on the leaf area index of the overstorey. For canopy drag
coefficients ranging from 0.05 to 1.5 they calculate values of d/h ranging from 0.43 to 0.82,
and values of z0m/h from 0.13 to 0.06 (section 4.1.5).
The ranges for 9?afl do not overlap for CM88 and MH95. The range in each derives from
variation in the location of the canopy source, but by quite different mechanisms. In CM88,
5Rafl depends on the height of the momentum source, (z0m + d), which varies in a fixed way
with LAI. In MH95, it depends on how the source is distributed, which is only partly related
to leaf area index. The CM88 model gives values at the lower end of the range in
intermediate canopies, with a drag coefficient of 0.2, while the MH95 values tend to be
smaller in denser canopies.
Also for SRfls the MH95 model has smaller resistance values, but this time the ranges
overlap slightly. The spread of values in MH95 derives mainly from uncertainty in the
diffusivity profile, while the spread in the CM88 values derives mainly from changes in
source height with changing canopy density. The lack of a common cause for the spread of
values predicted by each model is particularly disturbing, since each — for its own distinct
reasons — has 5RBS varying over a threefold range. Overall, the predicted values range from 6
to 60. This gives some indication of the uncertainty.
The boundary-layer resistance can't be described by simple representative values of
9?6 because it varies widely with leaf area index, leaf dimension and wind speed. The values
for each model are best described by formulae (Table 3.4). The SW85 model was designed for
a particular crop so its form was not intended to be general. Again the ranges calculated
using the CM88 and MH95 models do not overlap, though this time the difference is
principally through the choice of the ßs value in eq. 3.19. The range of values from the MH95
scheme would be 67-110 if they were calculated using ßs = 2 /3 , as in CM88. The remaining
difference originates from use of different averaging schemes and different exponents for
the canopy wind profile. The ranges of 91;, do not reflect the full uncertainties. The range of
values from CM88 is increased to 64-116 by varying the extinction coefficient for the wind
profile from 1.5 to 3.5. The ranges of 3ib are increased substantially in both CM88 and MH95
models if the uncertainty in ßs is included.
• Discussion
Also in comparison to the resistances in the MH95 model, the near-field resistor
introduced in section 3.2.2 is usually insignificant, and far-field theory is adequate for
building two-layer models, provided the far-field JC-profile is known correctly. Here
Raupach's suggested form for the far-field diffusivity profile was used, which is larger than
those used by SW85 and CM88, implying that the calculated far-field resistors are smaller. An
interesting question is how much difference this makes to calculated energy balances. In
• 8 6 Sparse canopy parameterizations for meteorological models
chapter 6 the impact of this difference is investigated using the coupled surface layer-PBL
models. Referring to the calculation of surface evaporation, McNaughton and Van den Hurk
(1995) state that the differences are important only when the evaporation rate is large
compared to available energy, the saturation deficit at reference height is high, and the
surface resistance of the canopy or underlying ground low. Also Dolman and Wallace (1991)
calculated very similar total evaporation rates from millet growing in Niger, using a
complete Lagrangian model, the Shuttleworth and Gurney (1990) two-layer model (nearly
similar to CM88), and the Penman-Monteith single-layer model. Saturation deficits and
evaporation rates are not notably high in that data set.
Another matter to comment on is the fact that MH95 have broken with the methods
introduced by SW85 and followed by CM88 and Shuttleworth and Gurney (1990) in that no
overstorey source is located at a fixed height. The idea that there is any necessary connection
between the distribution of scalar sources within the canopy and the parameters of the wind
profile were rejected. Instead, they integrated the diffusion equation directly for a
distributed scalar source, following the kind of methods pioneered by Cowan (1968).
Their results still rely on the quality of the far-field diffusivity profile used (eqs 3.5a
and 3.5b). Unfortunately, none of the field data of ow/u, which Raupach (1988) used to
construct these profiles extend down to the ground, and the two profiles from wind tunnels
that do so have a threefold range near the floor of the tunnel. Therefore profiles of ow are
poorly known near the ground. The T; profiles are even more uncertain. The diffusivity
profile is therefore unreliable near the ground, and the value of 9?as calculated from it has
great uncertainty.
Of particular concern is that we don't know how to describe JC-profiles near mixed
under-storey of bare soil and grass. This is disturbing because field results show that
temperature differences between bare soil and grass can be very large (e.g. Garratt, 1978).
Therefore we don't know how to construct a plausible model for transport from an
understorey, nor how to describe the excess resistance for sparse canopies. This is a serious
matter because excess resistance is needed to calculate heat fluxes from surface temperature
measurements made from aircraft or satellites (Bastiaanssen, 1995). The turbulence profiles
used here summarize profiles measured in canopies where little momentum reaches the
ground. That is, we expect that they apply only to rather dense canopies, for which the
profile area density exceeds 0.1 (Raupach, 1992). Fortunately, many 'sparse' canopies are
dense enough to satisfy this condition. It is difficult to build a model for very sparse
canopies with profile area densities < 0.1 because theory is currently inadequate and there
are no suitable experimental data for guidance. The two-layer model developed by
Shuttleworth and Gurney (1990) does 'extend' to very sparse canopies, but it does so simply
by interpolation between canopies with 'dense' overstorey, as modelled by CM88, and ones
where the overstorey vanishes.
The albedo of a sparse vineyard canopy during the growing season
Studies considering the energy balance of the Earth's surface involve the
quantification of the radiative energy supply, referred to as net radiation. This net radiation
consists of both longwave and shortwave terms. The latter contribution (0.3 - 3 pm) is to a
3. Aerodynamic transfer, albedo, and crop conductance 8 7 •
large extent determined by the reflecting properties of the surface, usually denoted as the
shortwave albedo or reflectance. Both the seasonal variation and the diurnal change of the
surface albedo can be of importance for describing the exchange of heat and water vapour
between the surface and the atmosphere. The seasonal variation is essential for
climatological studies and crop growth simulation models, whereas the diurnal variation is
important for short term weather forecasting and simulation of boundary layer
development. The shortwave albedo of a sparse canopy during part of its growing season is
the subject of the following sections.
Among the surface characteristics playing a major role for the shortwave albedo, an
important one is the fraction of plant cover, with a closed canopy or a completely bare soil
as the possible limits. The geometry of a closed canopy and the spectral properties of its
components can give rise to surface albedo values ranging between 0.10 and 0.25. Surface
roughness and content of moisture, organic materials and iron compounds in the upper soil
layer are important parameters for the albedo of bare soil, which can vary between 0.05 and
0.40 (Dickinson, 1983). A large part of the global surface is covered with sparse canopy. This
surface type is heterogeneous on a scale comparable to the individual vegetation elements,
but may well be considered homogeneous on a larger catchment scale. Due to the
complicated geometry and contribution both from bare soil and vegetation components, the
albedo of a sparsely vegetated surface depends on a large set of effects of the various
relevant surface properties.
The processes related to the surface albedo of the sparse vineyard canopy
endeavoured during the EFEDA-I campaign (section 2.2.3) is the subject of the following.
Albedo measurements were carried out in a period of rapid plant growth; the fraction of
vegetation cover increased from 0.05 (primarily bare soil) to 0.15 within a period of 25 days
(section 2.2.6). The diurnal and seasonal variation of the measured surface albedo are
explained from available theory and models. Also, the horizontal inhomogeneity of the
surface albedo on a scale of 200 x 200 m is discussed. For this purpose, remotely sensed data
are used.
3.3.1 Processes determining the albedo of a sparse vineyard canopy • The surface albedo
The shortwave hemispherical reflectance of a surface, or (surface) albedo, is defined
as the upward reflected part of shortwave (0.3 - 3 |im) radiation reaching a horizontal plane
on the surface. An incoming light beam I of wave length X from any azimuth direction 0O
and zenith angle Çg may partially be reflected upward in directions <|> and n = cos Ç. The
total albedo a is then obtained by considering the amount of reflected radiation from all
beams integrated over the hemisphere:
3 1 2n 1 2JC (3 21')
a = ƒ ƒ ƒ ƒ ƒ |J'-(<t>.|J^|<t)o.)1o)/(<l'0'^)d<l)dMd(l'odMod^ A. = 0.3MO = 0 * O = 0 1 1 = M , ' 0
where r(§, \i, X |<|>0, \ig) is the reflection coefficient of I(§0, \i0, X) into direction (<|>, n).
88 Sparse canopy parameterizations for meteorological models
• Shortwave reflectance of bare soil
Generally, soil reflectance increases as the wavelength increases from 0.3 to 3 |im
(Coulson and Reynolds, 1971). The amount of highly absorbing organic and iron
compounds in the soil have a pronounced effect on the reflectance in the visible range of the
spectrum. Beside this, other factors such as soil moisture content, zenith angle and the
structure of the top layer affect the albedo of a soil.
Dickinson (1983) discusses a model to describe the albedo of a flat soil, «s, constisting
of large distinctive particles. The model is based on a "delta-Eddington" approximation and
was used by Wiscombe and Warren (1980) to obtain the albedo of snow. Information is
needed about the reflectance of individual particles and the average angle of reflection. The
results show a clear dependence of soil albedo on zenith angle Ç. Generally more light is
reflected when the zenith angle is large, especially for flat dry surfaces. The zenith angle
response reduces considerably when the fraction of diffuse radiation, fd, is significant, and
thus depends on cloud cover and atmospheric turbidity. A simpler approach was followed
by Menenti et al. (1989), who used a semi-empirical relationship to describe the variation of
the bare soil albedo as with Ç:
asQ - a0{8(A,)]s^ (3-22)
In this equation, aQ is the albedo when the sun stands in zenith, A; is the optical depth of the
atmosphere in the direction of the solar beam, and g(A;) is a surface dependent function,
assumed to be a linear function of A;:
g (A,) =g0+cgA, (3.23)
where g0 and c are regression coefficients, to be obtained from field measurements. The
optical depth is defined by (Slater, 1980)
A; = - I n (3.24)
where K is the downward shortwave radiation at the surface level and the subscript e refers
to the extraterrestrial solar radiation. K /Ke is known as the transmission factor, the relative
amount of absorbed and reflected solar radiation by the atmosphere. Eq. 3.22 ensures that
as -» fl0 for Ç —> 0. a0 is surface specific and depends on values of humus and iron content and
moisture content in the top soil layer. In this simple approximation, the effect of increase of
the fraction of diffuse radiation, fd, with increasing Ç is implicitly included. The effect of a
change of/d due to cloud formation or changing atmospheric transmission is not
parameterized.
The moisture content of the upper soil layer is known to have a pronounced effect on
the bare soil albedo (Gräser and van Bavel, 1982; Idso et al., 1975). Wet soils reflect
shortwave radiation less than dry soils, and this difference can be as large as a factor five.
Gräser and van Bavel (1982) found that the albedo of three different types of soil changed
within a very small range of water potential, but remained constant when soil humidity was
3. Aerodynamic transfer, albedo, and crop conductance 8 9 •
outside this range. They conclude that the original Angstrom-theory, explaining the
reduction of reflectivity by trapping of radiation in the soil water films caused by a total
internal reflection, is consistent with the abrupt change of the albedo as soil moisture
changes. The soil moisture content of the top layer of the soil often shows a clear diurnal
cycle. Water vapour transported upward over temperature gradients and by capillary rise is
not removed by evaporation during the night. When the upper soil layer is dry, capillary
rise will be limited, but temperature gradients near the soil surface can be extremely large,
particularly when no vegetation is present. This effect combined with the process of dewfall
often results in a moisture content of the top soil layer which is higher in the morning than
at later times. In this case, the observed soil albedo shows an asymmetric response with
respect to solar time, being lower in the morning. The difference between morning and
afternoon albedo can be larger than 1.5%, as was for instance observed by Menenti et al.
(1989) above deserts. They applied an empirical correction for the lower albedo in the
morning (time t < 12:00 solar time), using a reduction factor md obtained from field
measurements. mä was expressed as linear function of sin Ç with coefficients md0 and cm:
md0 - cm s i nÇ t < 1 2 : 0 0 (3.25)
1 t > 12:00
Surface elevation differences can result in a variation of the soil moisture at many
scales. This effect, and the variability of the contents of iron and organic compounds, can
cause a strong horizontal variability of the soil albedo at scales ranging from a few cm to
hundreds of meters.
Wetting or roughening the soil decreases both the albedo and the sensitivity to solar
elevation. A near normal incident radiation can penetrate deeper into a coarse surface, and
becomes trapped by multiple reflections in the soil cavities. The laboratory studies reviewed
by Myers and Allen (1968) conclude that an increase of the soil particle diameter or
aggregation of particles into clumps reduces the reflectance of the soil, but that these
differences are usually overshadowed by the effect of differences in soil moisture and
humus content.
• Shortwave reflectance of plant canopies
The reflectance properties of plant canopies have been studied by many authors.
Dickinson (1983) gives a good review of most of the recognized factors affecting the albedo
of plant canopies.
Obviously, the reflectance and transmittance of individual leaves plays an important
role. These properties are a function of the wave length of the light. For simple purposes,
leaf reflectance p ; and transmittance x; are quantified as p; = x; = 0.15 for visible light (0.3 -
0.7 \im) and 0.4 for near infra-red (0.7 - 3 |jm) (Goudriaan, 1977). The leaf angle distribution
plays a role in the zenith angle response of canopy reflectance. If all leafs are in a horizontal
position, the reflection is independent of Ç. A canopy with e.g. spherically distributed leaves
reflects more radiation from lower angles of incidence. Closed canopies with multiple leaf
layers also tend to trap part of the reflected radiation, in particular at overhead sun. For low
• 9 0 Sparse canopy parameterizations for meteorological models
solar altitude this trapping is much less pronounced, and the canopy reflectance can increase
to 3 times its value around noon (Sellers, 1985; Goudriaan, 1977). On the other hand,
radiation above spruce forests with widely spaced spire-shaped crowns penetrates deeper at
large zenith angles (Dickinson, 1983). Finally, the degree of vegetation cover determines the
influence of the underlying soil upon the canopy reflectance.
A model for the albedo of a closed plant canopy plus its underlying ground, ac, was
developed by Goudriaan (1977) and also applied by Jacobs and van Pul (1990). Goudriaan
(1977) computed ac by regarding the decrease of the radiation with canopy depth as an
exponential function. For the albedo of a canopy with horizontal leaves, ahm, this resulted in
= a ~ ( 1 'a-asoil> -(floo-asoii>exP(-2K^1) ( 3 2 6 ) Ohor ~ l-a«,asoU-am(am-asoU)exp(-2krLAD
a„, is the albedo of the canopy when LAI —» ~, aSOT-; the reflectance of the underlying soil and
kr a semi-empirical extinction coefficient. Under the assumption that the reflectance of an
individual leaf, p;, equals its transmissivity t ;, and by definition of a scatter coefficient
O; = P; + T;, a^ is parameterized by
° ' (3.27) 2 0 + W - o ,
and kr = (l- cj)05. The scatter coefficient for visible light, ol OTS, is approximately 0.3, whereas
the value of 0.8 is adopted for the near-infra red value, o, m>. Also the reflectance of the
underlying soil, flS0I-;, must be specified for these bands separately.
The shortwave reflectance of a canopy with horizontal leaves does not depend on
zenith angle, as can be seen from eqs. 3.26 and 3.27. By contrast, for spherically distributed
leaf angles the canopy albedo, a h, depends on Ç. Goudriaan (1977) gives a simple
expression for a h, reading
_2 1 + 1.6 cos Ç V,(0="ftOr. .A...r W
The contribution of diffuse radiation to the albedo of a closed canopy can be
simulated using a weighted average of 3 direct beams with zenith angles 15°, 45° and 75°.
The weighing reflects the ratio of the projected areas of three band circles of a hemisphere
centred at these angles (Goudriaan, 1988). This yields
% A Vif) = 0.25 asph (15°) + 0.50 asph (45°) + 0.25 asph (75°) (3-29)
Assuming that the incoming shortwave radiation is roughly equally divided over the visible
and near-infra red bands, the albedo of a canopy is obtained by averaging the albedos of the
two bands a h vis and a h nir. Accounting for the fraction of diffuse radiation, ac is finally
expressed as
3. Aerodynamic transfer, albedo, and crop conductance 9 1
ac "ft
asph,vis(dif)+asph,mr(dif) "(!-ƒ*
f ^ aSph,vis^+asph,nir^ (3.30)
The reflectance of a closed canopy is generally lower than the reflectance of bare soil.
Trapping of radiation and strong absorption in the visible range cause this difference.
• The shortwave reflectance of a sparse canopy
By definition, a sparse canopy consists of both vegetation and a considerable part of
uncovered soil. Thus, the albedo of such a surface will depend on the soil moisture, texture
and iron content, on the geometry of the plant elements, the leaf density and leaf angle
distribution, on the position of the sun and the fraction of diffuse light. However, a few
special effects occur above sparse canopies with widely spaced plants.
First, a solar beam with a low angle of incidence will penetrate horizontally deep into
widely spaced canopy elements. However, a significant part will be reflected near the top of
the plants, where the angle of the beam to the normal of the canopy surface is large. This
effect makes the exact position of an albedo sensor far from trivial. Only far above the
canopy top the measured quantity can be regarded representative for the surface. Moreover,
the reflectance measured straight above a vine plant will depend more importantly on the
reflectance of the surrounding soil when the zenith angle is large. This makes interpretation
of albedo measurements of individual plant elements difficult.
Second, the shading of the soil by the plants will cause a reduction of the amount of
radiation reflected by the soil, especially in the visible range of the spectrum where the plant
elements absorb most radiation. This reduces the soil albedo, particularly at large zenith
angles and with dense plant elements, when much radiation is intercepted by the plants.
This shading effect will reduce the zenith angle response of the soil albedo.
Third, the large amount of radiation that penetrates into canopy elements at low
solar incidence obviously is associated with a reduction of the reflectance. The zenith angle
response of the albedo of a sparsely vegetated surface is therefore expected to be much less
pronounced than for a closed vegetation stand.
These effects formally imply that the albedo of a sparse canopy surface cannot
simply be expressed as a weighted average of the albedos of bare ground and of the
vegetation. The effects of vegetation on the albedo of bare soil will have to be incorporated
in parameterizations of as, and the influence of the presence of bare soil on the vegetation
albedo must be expressed in the equations for aQ. Only when these requirements are
satisfied, the average surface albedo can be estimated using a weighing over the fraction of
surface covered with vegetation, a& according to
a = Cy«c + (1 - oy)fls (3.31)
3.3.2 Albedo measurements taken in a sparse vineyard canopy
In this section the theoretical considerations listed above are evaluated using albedo
measurements conducted over a sparse vineyard area. Attention is paid to the issue of
horizontal variability, seasonal change and diurnal variation of the surface albedo. The site
• 92 Sparse canopy parameterizations for meteorological models
description and instrumental layout can be found in section 2.2. A brief summary of used
instrumentation is given first.
• Instrumentation
All shortwave radiation sensors were located in a single vineyard with distances of
10 to 100 m in between. Measurements were carried out well above the surface, above
parcels of bare soil, and above individual plants. Soil moisture measurements were taken
every 3 - 5 days using TDR at depths 0 -50 cm with 10 cm intervals. Table 3.5 lists the set-up
of these sensors.
Table 3.S: Acronyms of sensors measuring reflected shortwave radiation and soil moisture (TDR). The mast indication refers to the layout figure in section 2.2 (Figure 2.2; Table 2.1). WSC = Winand Staring Centre, WAUMET = Wageningen Agricultural University, Dept. of Meteorology, WAUHBH = Wageningen Agricultural University, Dept. of Hydrology
acronym
AH4
AH6
ABl
AB2
API
AP2
TDR
surface type
overall
overall
bare soil
bare soil
plant
plant
mast
s
ƒ
e
t
e
u
V
height/depth (m)
4
6
1.5
0.3
1.5
0.3
0.1,
m above
0.2, 0.3,
plant
0.4, 0.5
operating team
WSC
WAUMET
WAUMET
WSC
WAUMET
WSC
WAUHBH
Furthermore, an overpass of the NASA aircraft ER-2 carrying a Thematic Mapper
Simulator (TMS NSOOl) multispectral sensor at 29 June, 10:20 am, yielded reflectance data of
the measurement site with a resolution of approximately 18.5 x 18.5 m. Reflected radiation
was monitored in 7 different channels, enabling the derivation of a spectral albedo map of
the terrain. Calibration of the TMS albedo was carried out using six ground-truth
measurements in both the Tomelloso and the Barrax major sites. For details about the
procedure to obtain this map we refer to Bastiaanssen et al. (1993).
The albedo observed by the ground-truth sensors will be equal to the hemispherical
albedo defined by eq. 3.21, when a) these sensors are mounted exactly horizontal, b) its
cosine response is perfect, and c) the spectral response is constant within the shortwave
spectrum range, and zero outside this range. In practice, none of these conditions will
generally be met exactly. The albedo observed by the TMS NSOOl platform deviates stronger
from the hemispherical albedo due to the very small opening angle of the nadir viewing
• Spatial variability of observed albedo The heterogeneity of the albedo at a scale of the measurement site is clearly
illustrated by an albedo map constructed from data of the TMS NSOOl. The relevant
reflectance statistics of a square of 21 x 23 pixels with indicated coordinates are given in
Table 3.6. The square covers the measurement site of Figure 2.2 completely, and is totally
occupied by vineyard, apart from a few dirt roads. The TMS-data show that the albedo of the
3. Aerodynamic transfer, albedo, and crop conductance 93
site varies between 0.17 and 0.27 with a standard deviation of 0.017. The statistics show that
the variability between pixels is significant.
Three factors may explain the large heterogeneity of the effective surface albedo
observed with the TMS NSOOl. First, the horizontal variability observed by the remote sensor
may overestimate the variability of the hemispherical albedo (eq. 3.21). Radiation from large
reflectance angles are not detected by the platform, but can reduce the horizontal variability
considerably by spatial averaging. Second, the sandy loam soil had a red colour caused by
the presence of iron compounds. This colour was not uniform over the entire field, as could
be seen at the site. The iron content showed a clear variation, causing a variability of the
albedo, particularly in the visible range. Third, the field was not entirely flat. Estimated
height differences of about 0.5 m were observed on a horizontal scale of about 100 m. This
micro-relief might have caused local differences in the water content in the top layer, and
consequently differences in the mineralization of organic disposals. Darkness variations as a
result of this spatial variation induce a variability of the albedo.
Table 3.6: Statistics of TMS surface albedo map. The pixel resolution was 18.5 m; map size is 21 x 23 pixels
property value
UTM-coordinates
Western and Eastern border 505898 - 506305 (426 m)
Southern and Northern border 4332078 - 4332448 (389 m)
albedo values
minimum 0.173
maximum 0.271
average 0.223
median 0.223
standard deviation 0.017
• Seasonal variation
Figure 3.4 shows the course of the average albedo around noon, a0, as measured by
AH6 between 11.30 and 12.30 GMT, for the entire measurement period. The albedo early in
the period, applying to a very small vegetation cover, is typically 0.28. This value
corresponds with data for dry sandy soils cited by Ten Berge (1990). Feddes (1971) reports a
slightly lower albedo (0.24) for one case of dry sandy loam.
Due to the rapid increase of the vegetation cover a clear reduction of the surface
albedo was expected. This was for instance observed by Jacobs and van Pul (1990) above a
growing maize stand. On the contrary, except for a cloudy day (7 June) a gradual increase of
a0 is observed until day 19, followed by a sudden reduction and gradual changes after this
date. Measurements of the soil moisture content in the top 10 cm of the soil showed a very
gradual decrease until 21 June (from 0.055 m 3 /m 3 on 3 June to about 0.043 m 3 /m 3 on 21
June, see Figure 3.5) (Droogers et al, 1993). In spite of the fact that these measurements
cannot be considered representative for the moisture content near the surface, a reduction of
• 94 Sparse canopy parameterizations for meteorological models
the surface soil moisture may be deduced from Figure 3.5, which can possibly explain the
increase of a0 early in the period. Inspection of the albedos around noon measured by sensor
AH4 revealed an average difference of about -0.035 compared to AH6. This systematic
difference can be ascribed to local differences in the soil composition.
0.30-
0.25-
o?n-
+ + _ + + + + +
+ ** * ** *
plants API, AP2
-A ••"•
+ + +
* *
+ AH6
5« * ä K *
*
• •
• • • • - - - _ • • "
10 15 20 Date (June 1991)
25 30
Figure 3.4: +: Average albedo between 11:30 and 12:30 GMT measured at 6 m height above a sparse canopy, and above two individual plants (* and • )
Figure 3.4 also shows the albedo around noon measured above 2 individual plants.
The albedos differ by typically 2.5%. These differences are most likely caused by a different
albedo of the underlying soil, which significantly contributes to the measured albedo. The
long term variability resembles the observations by sensor AH6. As long as the plants cover
only a small part of the underlying soil the measured albedo increases, but a decline is
observed from 17 June onwards. This decline is somewhat stronger for the highest albedo.
Although the scatter is large and the measurements ended before complete vegetation cover
was reached, the data suggest that the two albedos tend to approach each other towards the
limit of a full vegetation cover.
Figure 3.5: Soil moisture content of upper 10 cm, measured using TDR (Droogers et al, 1993)
15 20 Date (June 1991)
3. Aerodynamic transfer, albedo, and crop conductance 95
• The diurnal variation
The zenith response of the albedo measured by sensor AH6 after noon changed
somewhat as the measuring period proceeded. Figure 3.6 shows the albedo measured by
AH6 at days 5,17 and 28 as function of zenith angle Ç, for afternoon data only. The selection
of days represents different stages of the plant growth. The zenith response of the albedo at
all days is very small for cos(Q > 0.5. This small response is associated with the rough
structure of the soil. Only when the zenith angle is large a clear response is observed.
The response increases as the vegetation covers more of the surface (day 28). This
response is shown to be stronger for the albedo measured overhead an individual plant
(Figure 3.6). Early in the season (day 5), when a large fraction of the measured upward
radiation is reflected by the surrounding soil rather than by the plant, the variation is less
pronounced. As the plants becomes denser and the surface albedo approaches the
characteristics of a closed canopy, the zenith angle dependence becomes stronger, and
observable at smaller zenith angles than for a bare soil.
1.00
Figure 3.6: The measured albedo after noon; Left: at 6 m height; Right: just overhead an individual plant for three different days in June 1991: day 5, day 17, day 28
In Figure 3.7 the diurnal courses of the surface albedo observed at 4 days with sensor
AH6 are shown. Day 5 represents fair weather conditions of a virtually bare soil. Days 20 and
21 are chosen as to represent a medium stage in the growing canopy, but with more clouds
on 21 June than on 20 June. At day 28 the canopy has almost reached its maximum size.
Also shown in Figure 3.7 are regressions obtained using eqs. 3.22 - 3.31. The albedo
for the plant area was computed by inserting the leaf area index per unit plant area, LAL, in
eq. 3.26. The coefficients entering the equations are obtained from the field measurements
and summarized in Table 3.7.
In Figure 3.7 the effect of clouds on the measured surface albedos is clearly present.
Clouds increase the fraction of diffuse radiation, which enhances the contribution of beams
with small elevation angles. Particularly at day 21, when cloud overpass occurred during
most of the day, the scatter around and after noon is larger than at the other days.
As time proceeded from day 5 to day 28, the assymetric response of the observed
surface albedo to the zenith angle gradually decreased. Possibly, the reduction of the albedo
in the morning is smaller at later times than early in the period, by a progressively declining
96 Sparse canopy parameterizations for meteorological models
moisture content in the top soil layer (Figure 3.5).
0.33-
0.31-
0.29-
0.27-
L
5 June
• ^ r
6
- ^ = ^ = > j j > " "
8 10 12 14 Time (GMT)
•
" / " ^ r
16 18 2! 10 12 Time (GMT)
10 12 14 16 18 20 Time (GMT)
10 12 14 16 18 20 Time (GMT)
Figure 3.7: •: Diurnal courses of albedo measurements using sensor AH6 at 4 different days in June 1991; regressions of data using eqs. 3.22 - 3.31 and the coefficients listed in Table 3.7
3.3.3 Conclusions
The albedo of the sparse vineyard canopy shows a variation at different scales, both
in time and in space. The large scale time variation includes a gradual increase of the albedo
around noon caused by drying of the soil, and a slight decrease related to the development
of the vegetation. These simultaneous and counteracting effects resulted in a rather
conservative value of a0, for which 0.285 ± 0.005 is a reasonable estimate. The dependence of
surface albedo on zenith angle and — possibly — soil moisture fluctuations are causes of a
diurnal variation which exceeds the variability of a0. Most of this variation is observed at
large zenith angles, and therefore has a limited impact on the net radiation balance. Also
clouds can give rise to sudden albedo changes by a change of the fraction of diffuse
radiation. Considerably larger is the spatial variation at the scale of a single field, caused by
differences in soil composition and water content. Smaller scale spatial variations originated
from different reflectance properties of the plant elements and the open bare soil spaces in
between.
3. Aerodynamic transfer, albedo, and crop conductance 97
Table 3.7: regression coefficients applied to eqs. 3.22 - 3.31
parameter
bare soil albedo around noon
offset of zenith response function
slope of zenith response function
offset of asymmetry function
slope of asymmetry function
leaf area index per unit plant area
fraction of vegetation cover
symbol
a0
So
CS
md0
cm
LAI,
°f
equation
3.22
3.23
3.23
3.25
3.25
3.26
3.31
value at
5
0.284
0.96
0.2
1.06
0.12
3.0
0.05
day
20
0.292
0.96
0.2
1.06
0.12
4.2
0.09
21
0.292
0.96
0.2
1.06
0.12
4.2
0.10
28
0.292
0.96
0.2
1.06
0.12
3.9
0.13
3.4 A photosynthesis model for the crop conductance applied to a sparse vineyard canopy
To describe the exchange of water vapour between the land surface and the
atmosphere many meteorological models use a so-called crop conductance (gc), or its
reciprocal crop resistance (r$c), which expresses the efficiency of water transport from the
substomatal cavities in canopy leaves to the ambient air. This crop conductance can be
considered as a physiological parameter, since it is mainly determined by the behaviour of
leaf stomata. Models describing the crop conductance usually include a dependence on
various environmental parameters, in particular light intensity, humidity of the ambient air,
leaf temperature and soil moisture availability (see for instance Dolman and Stewart, 1987;
Stewart, 1988; Noilhan and Planton, 1989). Very often statistical regression of stomatal
conductance data on values of environmental parameters is used to obtain a mathematical
prognostic model for the crop conductance (Jarvis, 1976; Stewart, 1988). Functions for each
parameter are then simply multiplied to yield a prognostic expression for gc:
8c - 8s,maMl • /i(*i> • /2(*2> • • - • ƒ„(*„) ( 3-3 2 )
In this expression gs is a maximum stomatal conductance, and^x,-) expresses some
functional dependence of gc on environmental factor xt.
Since water vapour evaporated from substomatal cavities is transported along an
identical pathway as the C02-transfer associated with photosynthesis, other workers
determine the crop conductance by parameterizing a leaf stomatal conductance gs as
function of the photosynthetic rate. Some algorithm to scale up gs to the conductance at
canopy level, gc, is then adopted. A stomatal conductance for C02-transfer, gs C 0 2 , is defined
as the ratio of the net C02-transport between the ambient air and the leaf stomata, FC02, and
a difference between the CC^-concentration within the stomatal cavities, C;, and in the air
directly surrounding the leaf, Cs:
98 Sparse canopy parameterizations for meteorological models
g rn = C°2 (3-33) °s,CU2 r - c
s i
An analogy is assumed between the stomatal conductances for water vapour and for C0 2 :
is = ^Ss,COl <3.34)
where the factor 1.6 accounts for the difference between the molecular diffusivities of both
gases. In practice, the C02-transport is governed by the net leaf photosynthetic rate.
Following this approach a model for gs is assessed by using a model for the leaf
photosynthesis, An, and adopting some assumption for the concentration gradient Cs - Ct
(see, e.g., Goudriaan and Van Laar, 1978; Wong et al., 1979; Goudriaan et al., 1985; Jacobs,
1994). This type of model is hereafter referred to as a An-gs model. Since these models
consider a physical and physiological mechanism for gas exchange between plants and
ambient air, they gain significant generality compared to the statistical models.
Field and laboratory observations reveal that the stomatal conductance shows a
dependence on ambient humidity. Although the mechanism of this response is not
completely resolved, a reduction of gs is usually observed as the ambient humidity deficit,
Ds, increases (see for instance Turner, 1991; Morison and Gifford, 1983), and this effect can
even result in a reduction of the plant evaporation, in spite of an increase of the humidity
gradient (Choudhury and Monteith, 1986). In recent studies the dependence of gs on D$ was
incorporated in a An-gs model by a number of parameterizations. Jacobs (1994) proposed to
express Cs - C, as a function of Ds. Alternatively, Kim and Verma (1991a) first calculated gs
without including humidity effects, and adopted an empirical adjustment of the
conductance as function of Ds afterwards. This approach resembles the semi-empirical
Jarvis-type model (eq. 3.32), and various shapes of these response functions were proposed
(Kim and Verma, 1991a; Winkel and Rambal, 1990).
The aim of this section is to evaluate the parameterization of the crop conductance of
a sparse Mediterranean vineyard canopy using a photosynthesis approach. The leaf
photosynthetic rate was calculated using the photosynthesis model of Goudriaan et al.
(1985). Three different parameterizations of the response of gs to air humidity (Jacobs, 1994;
Kim and Verma, 1991a; Winkel and Rambal, 1990) are explored using leaf conductance data
collected in the context of the EFEDA research program. A simple weighing scheme is used to
scale up modelled leaf conductances to the canopy scale, for practical applicability in large
scale meteorological models. Leaf conductance data were aggregated to a crop conductance
using a similar weighing procedure, and model results are compared to data at the canopy
level.
3.4.1 Theory • The An-gs model and parameterization of humidity response
In the An-gs model, gs is calculated by adopting a model for An = FC02 in eq. 3.33,
and using an explicit parameterization for Cs - C,. The net photosynthetic rate An is a balance
between the gross photosynthetic rate and the losses due to photorespiration and dark
respiration. Goudriaan et al. (1985) developed a model to describe An for a leaf as function of
3. Aerodynamic transfer, albedo, and crop conductance 9 9 •
the amount of absorbed PAR by the leaf, its temperature, T;, and the ambient C0 2 -
concentration, Cs. A distinction was made between the different metabolisms of C3 and C4
plants. Details of the algorithm for An can be found in Appendix IV.
The parameterization of Cs - C; by Jacobs (1994) is based on a strong correlation often
found between the photosynthetic rate and the leaf conductance under a wide range of field
circumstances. The strong correlation is related to a conservative ratio between C; and Cs, as
observed by e.g. Goudriaan and Van Laar (1978) and Wong et al. (1979). This conservative
behaviour is thought to reflect the plant's strategy to optimize the relation between water
use and C02-assimilation (Cowan, 1982). Some workers found the ratio Ci/Cs to decrease
with ambient humidity deficit (Wong et al., 1979; Morison and Gifford, 1983). Regarding eq.
3.33, this implies that apparently An (= FC02) exhibits a smaller response to increasing
humidity deficit than gs. Jacobs (1994) and Jacobs et al. (1995) used this result to
parameterize humidity responses of gs. They prescribed Ci/Cs as a linear function of the
ambient humidity deficit Ds. Accounting for the effect of photorespiration on C;, the
following relationship was used:
c,-r Cs
D„
max
(3.35)
where T is the C02-compensation concentration, and f0 and Drmx calibration coefficients (see
Appendix TV for details).
In the approach of Kim and Verma (1991a,b) the ratio (C; - T)/(CS - T) was fixed at a
constant maximum value. A maximum stomatal conductance, identified as gs , is obtained
by inserting this value in eq. 3.33. An empirical curvilinear humidity response function was
applied to obtain the actual value of gs, according to
O l ,„ ~r\
in which bD is a calibration coefficient, remaining to be specified. The value of
(C, - r ) / (C s - r ) is taken equal to 0.85 in the present analysis (Morison and Gifford, 1983; see
also Appendix IV).
Winkel and Rambal (1990) experimentally determined the stomatal conductances of
various grapevine species, and used an exponential humidity response function for gs. Their
expression for gs was of the form
S s = S ° e x p ( - D , / D r ) <3-37>
where again gs° is used to indicate the value of the stomatal conductance obtained without
including a humidity response, and Dr is another calibration coefficient.
• Scaling up from leaf to crop For use in large scale meteorological applications, a one-layer description of the crop
conductance must be derived from a model for gs, using a weighing scheme for various
microclimate classes of the canopy leaf population. Particularly the response of gs to
• 100 Sparse canopy parameterizations for meteorological models
absorbed PAR is highly non-linear. Leaves which are not directly illuminated by the sun
contribute relatively much to the canopy photosynthesis, due to a very efficient use of light
(Goudriaan, 1977). Following Baldocchi et al. (1987), gs is calculated for two microclimate
classes: the sunlit and shaded regimes. A simple weighing scheme using the sunlit and
shaded leaf area, LAIsun and LAI$had, is applied to define an average crop conductance:
ic = ^ S J S U + ws< w (3-38)
where Ia is the amount of absorbed PAR, and the subscripts sun and shad denote the sunlit
and shaded regimes, respectively. Values of leaf temperature, ambient C02-concentration
and humidity deficit are assumed similar for shaded and sunlit leaves.
Using the An-gs model outlined in eqs. 3.33 - 3.35, and the weighing scheme in eq.
3.38 to determine the crop conductance gc, the environmental parameters that need to be
specified are LAIsun and LAIshad, Ia sun and Ia shaä, and leaf temperature, ambient C0 2 -
concentration and humidity deficit.
For the distribution of total leaf area LAI over sunlit and shaded fractions simple
semi-empirical equations (e.g., Campbell, 1977) are succesfully applied for closed canopies.
However, grouping of leaves in clusters — as is the practice in sparse canopies or row
crops — makes these closed-canopy formulations invalid. In the present study the fraction of
sunlit leaf area, ƒ = LAIsun/LAI, was derived from field measurements (Figure 2.9), and will
be further addressed in the discussion. Also the values of T;, Cs and Ds were obtained from
measured quantities, in a way explained in Appendix IV.
Norman (1982) proposed simple expressions to describe the flux densities of PAR
reaching the sunlit and shaded leaves separately, as function of incoming PAR at reference
height, LAI and solar zenith angle Ç. Assuming a random distribution of leaves over the
canopy without azimuthal preference, and a spherical leaf angle distribution, the amount of
absorbed PAR (Ja) for each class is given by
la*had = a!PARs/wd ( 3 3 9 )
PAR^exp(-0.5 M / 0 7 ) + 0.07 PARdl> (1.1 - 0.1 LAI) exp(-cosQ
h^un = « /P A Rs«„
0.5PARdl>
• P A R s M
v cosÇ
(3.40)
Here, PARsfeld and PARsun are the average flux densities of PAR reaching the shaded and sunlit
leaves, and a, is the leaf absorbtivity, taken as 0.8 (Kim and Verma, 1991a). Direct and
diffuse PAR, denoted by the subscripts dir and dif, respectively, are assumed to be a constant
fraction (0.47) of incoming direct and diffuse shortwave radiation (Goudriaan, 1977).
3.4.2 Site description and measurements
The analysis of the A -gs model and the humidity response of the crop conductance
is carried out using Mediterranean vineyard data measured during EFEDA-II. Measurements
of LAI,fs, gs, total evaporation (E), average C02-concentration, friction velocity u», wind
3. Aerodynamic transfer, albedo, and crop conductance 1 01 •
speed u, air temperature (Tfl) and specific humidity (qa), and incoming shortwave and
diffuse radiation {K and Kdiß were measured as outlined in the previous chapter. Leaf
conductance data were averaged per hour to yield values of crop conductance gc according
to a weighing scheme similar to eq. 3.38 (see section 2.3.6). Leaf temperatures recorded by
the diffusion porometer were arithmetically averaged per hour, separately for sunlit and
shaded leaves. Also PAR measurements were recorded using the porometer sensor, held in
approximately the same orientation as the leaf being monitored. Separate hourly averages of
PAR were computed for shaded and sunlit leaves.
All meteorological measurements were averaged to hourly values, in correspondence
with the porometry averaging interval. Timing between the energy balance and the
porometry measurements was accurate within 1 minute.
3.4.3 Results
• Calibration of the humidity functions
The An-gs model as proposed by Jacobs (1994) and Jacobs et al. (1995) was calibrated
during a field experiment carried out in 1991 in La Mancha, Spain, in the context of EFEDA-I.
That site and vegetation were very similar to the location explored in the current study. For
the calibration of the An-gs model and the humidity response function (eq. 3.35), Jacobs
(1994) used measurements taken with a steady state gas exchange unit, measuring the total
C02-transport to a leaf, PAR, leaf temperature and Ds. He assumed the crop to be well
supplied with soil moisture, owing to the large rooting depth of the vine plants. Since no
explicit description of the dependence of gs on soil moisture availability is considered, any
possible effect of soil water depletion is implicitly included in his calibration of the model.
The resulting calibration coefficients can be found in Appendix IV.
1.6-
1.4-
1.2-
1.0-
go» 0.6-
0.4-
0.2-
o.o-
m
m •
1
^ \
r--' i i 1 T • r
-
• " •
" 10 15 20 25 30
Ds (g/kg) 35 40 45 50
Figure 3.8: Measured values of gc normalized with gc plotted against specific humidity deficit Ds. Also shown are the best-fit functions given by eqs. 3.36 (bD = 0.121 (g/kg)"1, - - - ) and 3.37 (Dr = 17 g/kg, )
The calibration of the curvilinear (eq. 3.36) and exponential (eq. 3.37) humidity
response functions was carried out directly at the canopy level. First, a maximum stomatal
conductance, gs , was computed for the sunlit and shaded leaves separately, and these were
aggregated to a maximum crop conductance, gc , using the weighing scheme of eq. 3.38.
102 Sparse canopy parameterizations for meteorological models
Figure 3.8 shows a plot of observations of gc normalized by gc plotted against Dg. The
optimal curvilinear fit of eq. 3.36 was found to be represented by adopting bD = 0.121
(g/kg)"1, while the optimal value for Dr appearing in eq. 3.37 was found to be 17 g/kg. Both
functions are also shown in Figure 3.8. The curvilinear function overestimates gc/gc° at high
values of Ds, and underestimates this ratio at low humidity deficit. A better agreement is
obtained when an exponential function is applied.
• The crop conductance from the An-gg model Figure 3.9 shows a 1:1 plot of the measured and calculated crop conductance gc,
using the humidity response proposed by Jacobs (1994, eq. 3.35). From a linear regression
through the origin, the model for gc overestimates the experimental values on the average
by 14%, and explains r2 = 58% of the variance.
12-
10
jr 8-
E
8. &
3 fc 4-
2-
o-
A
A ' A A-
A 4.
^ * A ^ A
A
A
A ^
*A
AA A
A
A
A *
A /
jf A
k A A *
A
, ! !
Figure 3.9: Measured and calculated values of crop conductance gc, using the humidity response function of Jacobs (1994) (eq. 3.35)
4 6 8 measured gc (mm/s)
10 12
A similar plot for the curvilinear function (eq. 3.36) results in a fairly low value for r2
(30%). As expected, low values of gc (corresponding to a high specific humidity deficit) are
significantly overestimated, and this is compensated by an underestimation at higher
conductances. A better agreement is obtained when the empirical curvilinear function is
replaced by the simple exponential function (eq. 3.37). Using Dr = 17 g/kg, the model
explains r2 = 68% of the variance (figures not shown).
Figure 3.10 shows the diurnal variation of the observations and the three model
variations for four different days, selected as to cover a wide range of days spread over the
measurement period. It is clearly seen that gc decreases with time, both at a diurnal and a
seasonal time scale. The exponential fit and the expression of Jacobs (1994) show a close
correspondence for most cases. The linear fit tends to overestimate gc in the afternoon,
particularly at later days.
3.4.4 Discussion and conclusions Values of gc, modelled using a photosynthesis approach and a response to ambient
humidity proposed by Jacobs (1994) calibrated for a similar crop three years earlier, and by
3. Aerodynamic transfer, albedo, and crop conductance 103
adopting simple procedures to express PAR and Ds, showed a fair agreement with observed
values of the crop conductance. Preliminary calculations showed that values of r2 are much
better than the performances of models using a statistical regression of gc on Ds also
calibrated in 1991. More attention to a comparison between the An-gs model and a statistical
approach will be paid in a subsequent study.
Particularly at small values of gc the crop conductance predicted by the An-gs model
is somewhat overestimated. The model results are rather sensitive to the value of the
ambient humidity Ds. The method to obtain Ds is associated with errors in measurements of
E, qa and u„, and the assumptions concerning the turbulent exchange between the reference
level and the leaf surface (Appendix IV).
day 163 day 194 B-
5
•
$ E E. a
& 2
1-
00 00
A// \CT
f A - ^
06:00
A
12:00 18:00 00
time (GMT)
5
4
fc E a 8>
2
Ï
0
A {
\ A
v ^ '
day 173
A
~ A ^ \
A V
1 ,
day 205
00:00 time (GMT)
06«) 12:00 18:00 time (GMT)
Figure 3.10: Measured and calculated values of crop conductance gc, for DOY 163, 173,194 and 205; A observations; modelled gc using the humidity response function of Jacobs (1994) (eq. 3.35); the curvilinear humidity response function (eq. 3.36) with bD = 0.121 (g/kg)"1; the exponential humidity response function (eq. 3.37) with Dr = 17 g /kg
Replacing modelled PAR by porometer observations did not result in a significant
improvement of the correlation coefficient. The average overestimation of calculated values
of gc was reduced from 14% to 12% (figures not shown), in spite of the noticed
underestimation by the PAR equations. The difference between modelled and measured PAR
was especially present at high radiation levels, where the sensitivity of the photosynthesis
104 Sparse canopy parameterizations for meteorological models
model to the amount of absorbed PAR rapidly falls off (see eq. 3 in Appendix IV). This
implies that also the sensitivity of predicted values of gc to the parameterization of
intercepted PAR is less significant at high radiation levels.
Also, the measured values of gc are subject to variability due to sampling errors.
According to the porometer manufacturer the sampling error of a single porometry
measurement is approximately 20%, owing to incorrect temperature or humidity
registrations in the porometer sampling cell, or to improper field calibration. The error
involved with scaling up leaf conductances to the canopy level depends on the sampled and
true distribution of leaf conductances of a single plant, the representativity of the selected
plants in the field, and the errors in the estimation of the leaf area index, fraction of sunlit
leaves and the determination of leaf age. The coefficient of variance (cv - o(gs) I g~&, where
~gs is the average leaf conductivity) of the porometry measurements within a single
averaging interval (1 hour) can serve as an indication of the error associated with the total
crop conductance assessment. The cv increased from 0.35 ± 0.15 in the first half of the
measurement period to 0.50 ± 0.25 in the second half.
Another possibly important source of error of the An-gs model is associated with the
calibrations carried out by Jacobs (1994). He assumed his crop to be well-watered, and soil
moisture depletion was not included in the parameterization for gc. However, a very low
soil moisture content during long periods of time may affect the stomatal conductance
negatively (Turner, 1991). There is accumulating evidence that stomatal response to soil
water drought is governed by a change of the metabolic products in the xylem sap. This
implies that soil water stress extending for a significant period will reduce the stomatal
conductance of a crop. Soil moisture conditions may well have been different during the
current experiment compared to the conditions reported by Jacobs (1994), and a shortage of
soil water possibly reduced the actual crop conductance. In this situation, the model will
overestimate the true conductance values. Unfortunately, soil moisture data necessary to test
this hypothesis were not available.
A simpler approach to include the response of gc to ambient humidity deficit, as
proposed by e.g. Kim and Verma (1991a,b), required the derivation of a crop conductance
not affected by an ambient humidity deficit. For this, a value of gc was computed using
(Cj - r ) / (C s - T) = 0.85 (see Appendix IV). Two different humidity response functions were
optimized, using the current dataset rather than being tested independently. An optimal
curvilinear fit to the measured conductance data was achieved for bD = 0.121 (g/kg)"1. This
value is rather high compared to the range reported by Kim and Verma (1991b) for three
tallgrass species (0.01 - 0.03 (g/kg)"1). A strong humidity response of the vine species
considered in this study is also revealed using the exponential function, which showed a
better correspondence than the curvilinear fit. The value of the empirical coefficient D r = 17
g /kg found from the present results also points at a strong humidity response compared to
the results of Winkel and Rambal (1990), who report Dr <= 48 g/kg for Carignane vine. They
suggest that the stomatal humidity response is a species dependent characteristic, which
might be linked to its geographical origin. Carignane — originating from the Aragon region
in Spain with a strong semi-arid climate, and well-known for its hardiness — shows a
relatively strong humidity response when compared to a species originating from the Rhone
valley (Shiraz, Dr = 222 g/kg). A strong humidity response is likely to be favourable under
3. Aerodynamic transfer, albedo, and crop conductance 1 05 •
dry circumstances in order to avoid excessive water loss, and increases the water use
efficiency of a crop. The even stronger humidity response encountered in the current study
may be related to a stronger soil moisture stress, but this assumption can not be validated
here.
In order to apply a photosynthesis model in large scale meteorological applications, a
simple weighing procedure was adopted from Baldocchi et al. (1987), which requires an
establishment of PAR absorbed by both shaded and sunlit leaves, and a factor representing
the weight of each leaf class. In the current study the fraction of sunlit leaves, ƒ , was
obtained from field measurements. Practical formulations for fs have been proposed for
closed canopies (e.g., Campbell, 1977), but are invalid for sparse canopies. However,
application of these formulations with effective leaf area indices can often result in
reasonable descriptions. For instance, the simple equation of/s proposed by Campbell (1977)
overestimated observed values of/s considerably when measured LAI (0.25 m 2 /m 2 ) was
inserted. A reasonable estimate of fs was given by using a tenfold value for LAI.
The An-gs model of Jacobs (1994) and Jacobs et al. (1995), incorporating effects of air
humidity deficit on gc via a modified CJCs-ratio, is a relatively simple and promising
approach for calculating the crop conductance gc of species similar to the vines studied here.
However, the sensitivity of gc to ambient humidity varies widely between different plant
species and even between vine cultivars. This variability imposes severe limitations on the
use of uniform humidity response functions in any conductance model for large scale
applications. The calibration carried out in 1991, however, seemed to be well applicable to
the new 1994-dataset.
Monteith (1993,1995b) and Mott and Parkhurst (1991) suggested thatgc should be a
function of the crop evaporation rather than of the ambient humidity deficit. Monteith
proposed to express the canopy conductance as function of the crop evaporation rate, using
two scaling parameters, gmax and Emax:
S E &c = 1 - f_ (3.41)
max
He hypothized that gmax is a function of the crop photosynthetic rate, and Emax is related to
soil moisture. A possible strategy to obtain gmax is to use the An-gs model described in this
section under conditions where Ds = 0 and so (C, - T)/(CS - T) = 0.85. Based on the measured
crop conductances described in this section, this assumption was used to explore the
behaviour of E1mx. However, owing to the sparse vegetation, relatively low values of the
surface evaporation, and the lack of soil moisture measurements, the results were not fully
conclusive. More evidence of eq. 3.41 is needed before it can be used in meteorological
models.
3.5 Conclusions
In this chapter three aspects of surface exchange for a sparse canopy are discussed.
The first aspect, the aerodynamic transfer between the surface and the atmosphere, has
resulted in the formulation of a new set of aerodynamic resistances, based on Lagrangian
theory. Also, these resistances are no longer parameterized by use of a fixed hypothetical
• 106 Sparse canopy parameterization^ for meteorological models
source at d + z0m, but include an 'effectiveness weighing', which accounts for the effect of a
vertical source variability. These resistances are presented in normalized forms, and scale
with «». They are developed for a two-component surface model, and as such can be used to
describe the exchange between the atmosphere and a sparse canopy. These resistances will
be included in the one-dimensional simulations in chapter 6, and compared to existing
formulations in a coupled SVAT-PBL model.
The survey of the surface albedo of the EFEDA-I measurement site has revealed a
considerable variability, both in time (at diurnal and seasonal scale) and in space (at scales
ranging between the diameter of individual plants and TMS-NSOOl pixel size). An empirical
regression was carried out to account for the temporal variation. The temporal changes at a
seasonal time scale were rather low, probably owing to the counteracting effects of
increasing vegetation cover and decreasing soil moisture content. In the remainder of this
study, the effect of this temporal and spatial variability on the land surface-atmosphere
interaction is not further investigated.
The An-g$ model of Jacobs (1994), describing the leaf stomatal conductance, was
upscaled to the canopy level. The formulation of the canopy resistance from this work will
be included in the sensitivity analysis in chapter 6.
3. Aerodynamic transfer, albedo, and crop conductance 1 0 7
4 A model is a mathematical interpretation
of a physical process,
rather than a second reality
Selected surface layer and boundary layer models
This chapter briefly describes the models used for the 'zero-dimensional' SVAT-
intercomparison in chapter 5, and the sensitivity analysis with coupled SVAT-PBL models in
chapter 6. As was outlined in the introduction of this thesis, components of various existing
SVAT's will be combined in that sensitivity chapter. In spite of this, the existing surface
models will be discussed here in their most original form, although a few modifications to
authentic papers were employed. This particularly holds for the suggestions proposed by
Van den Hurk and Beljaars (1995) to improve the new ECMWF surface scheme developed by
Viterbo and Beljaars (1995). A separate section is dedicated to these suggestions.
After the discussion of the surface models in section 4.1, two models for the PBL are
briefly outlined in section 4.2. A list of model limitations is discussed in section 4.3.
All models were extensively described in the original literature. In the following
sections only the essentials will be presented.
4.1 Surface layer models for sparse canopies
Various parameterizations are currently in use in large scale GCM's or numerical
weather prediction models. The degree of complexity varies from simple one-layer schemes
inspired by the 'big-leaf' model (Monteith, 1965), to sophisticated multiple-source models
(for instance, Sellers et al., 1986; Dolman, 1993). Detailed multiple-level canopy models
(Waggoner and Reifsnyder, 1968; Goudriaan, 1977; Raupach, 1989a, 1989b; El-Kilani et al,
1994) are usually too complex to be used in large scale applications, owing to a large
demand of input information and computer time. These models are not addressed here.
In the following sections the selected models are briefly described: a form of the big-
leaf model, the ECMWF-surface scheme and its modifications, and the two-layer models of
Deardorff (1978), Shuttleworth and Wallace (1985) and Choudhury and Monteith (1988).
Some of these models do not include a specific description of the canopy resistance, rsc, but
• 108 Sparse canopy parameterizations for meteorological models
rely on the parameterizations for rsc developed independently. The rs
c-parameterizations of
Viterbo and Beljaars (1995) and Choudhury and Monteith (1988) are discussed in the
sections covering their surface models. The scheme proposed by Noilhan and Planton (1989)
is treated in section 4.1.4, containing the model of Deardorff (1978). The parameterization of
rsc along the lines of the photosynthesis-^ model of Jacobs (1994) is presented previously in
section 3.4. Also the implementation of Lagrangian diffusion theory (McNaughton and Van
den Hurk, 1995) was discussed before (section 3.2), and this will not be repeated here.
4.1.1 The modified big-leaf model
The well-known one-layer 'big leaf' model (Monteith, 1965) simply describes
evaporation and sensible heat exchange between a single surface and a reference level at
height zR close above. Strictly speaking, it is not applicable to sparse canopy surfaces, since it
does not include a separate treatment of the various components of a sparsely vegetated
surface. However, because of its simplicity it is present in various GCM's and NWP-models.
For that reason it is included in the comparison study in chapter 6.
The original 'big leaf' model does not include a description of soil heat flux. For
many sparse canopies this is a major term in the surface energy balance. In the formulation
presented below, the soil heat flux is parameterized using a slightly modified so-called
force-restore method.
The big-leaf model considers the energy balance of a surface (eq. 1.1), rewritten as
A = Qt-G = H + XE (4.1)
where A is the available energy. Application of eq. 4.1 to a canopy assumes that no energy is
stored or released within the canopy (either in the biomass or in the air within the canopy
layer). Also, energy used for photosynthesis or respiration processes is ignored.
The turbulent fluxes of heat and water vapour are commonly expressed as ratios of a
gradient of the scalar (temperature or water vapour density) and some resistance for
turbulent exchange between the surface and zR, denoted by ra, according to
H = p c „ ! f ^ l ! l (4.2)
and
1 r ~-i 1s<tiS*sur> 4'a .„ „. Kb = pA. (4.3)
where Tsur (or Qsur) is an effective surface (potential) temperature (section 2.4.2), and 0fl and
qa are the potential temperature and specific humidity at the reference level zR. Latent heat is
supposed to be released from the surface through numerous stomatal pores present in
canopy leaves. It is assumed that the specific humidity within these stomatal cavities is at
surface temperature saturation, and in eq. 4.3 an additional resistance is included for the
water vapour transport, being the 'surface resistance' rsc. This resistance allows for stomatal
control of evaporation by plant canopies (Monteith, 1965), and must be explicitly
4. Selected models 109 •
parameterized.
The aerodynamic resistance for heat and water vapour, rfl, consists of two parts:
a h ra = ra+ra
(4.4)
The first, r", is a (stability dependent) exchange resistance between the reference level and
the momentum roughness length, z0m. For neutral conditions, the resistance is equal to the
exchange resistance for momentum transfer. For stable and unstable conditions rfl" is given
by
r„ = « . K
In *0m
- ¥» • ¥ . '0m (4.5)
where ^¥n is a stability correction as function of the Monin-Obukhov length L (Beljaars and
Holtslag, 1991).
The second part, rfl , is a (semi-empirical) excess resistance to account for the absence
of bluff-body forces for scalar exchange (Garratt and Hicks, 1973). This latter resistance is
equivalent to adopting a roughness length for scalars, zoh, which is smaller than z0m. The
excess resistance is given by
KM In
z0m
K0hP
(4.6)
where stability effects are ignored. Other parameterizations of ra are based on the concept
of a so-called leaf boundary layer resistance (Gates, 1980). More on this issue will be
discussed below. At the outset we take rfl equal for heat and moisture exchange.
Net radiation is a (weak) function of the absolute surface temperature, Tsur,
according to
Q, =(l-a)Kl+Ll-eaT4sur
(4.7)
Incoming longwave and shortwave radiation, as well as the surface albedo and emissivity
must be explicitly provided.
When a realistic description of the entire energy balance is needed, an expression for
the soil heat flux G must be carried also. In this study the big-leaf model is extended by an
equation for G, derived from the so-called 'force-restore' method (see section 4.1.4). G can be
found from the rate of change of the surface temperature, T$ur, and a deep soil temperature,
?2-
G = P'Chdi
i^a
9T„ 27t T . r2) dt "1
(4.8)
where p'Ch is the volumetric heat of the soil, d1 is the e-folding depth of a diurnal
• 110 Sparse canopy parameterizations for meteorological models
temperature wave, and i j is the length of a single wave (see below). By rewriting the force-
restore equation in this form, the surface energy balance equation can easily be solved by
solving for Tsur For small timesteps, only a small numerical difference exists with the
original force-restore method, in which Tsur from the previous timestep is taken to solve the
surface energy balance (see Appendix V).
For a given r$c and forcings at reference height, eqs. 4.1 - 4.8 can be solved iteratively
for the surface temperature Tsur using the Newton-Raphson scheme (Jacobs and Brown,
1973; Appendix V). The stability correction in eq. 4.5 should be accounted for in another
iteration loop, or computed by taking Lv from the previous time step.
This description of the big-leaf model is just one of the possible forms which are
found in literature. Possible variations can be applied to the parameterization of soil heat
flux (e.g., De Bruin, 1982), excess resistance (Kustas et al., 1989), parameterization of
incoming longwave radiation (Brutsaert, 1982), or stability corrections to aerodynamic
resistance (Inclân and Forkel, 1995). Other workers included extensive schemes for surface
albedo, canopy resistance, heat storage within the canopy and other issues. The formulation
presented here serves the compatibility with other surface models, in order to be able to
compare surface model components adequately (chapter 6).
4.1.2 The ECMWF surface scheme
• Model description The recently updated ECMWF surface scheme (Viterbo and Beljaars, 1995, replaced by
VB95 hereafter) contains a rigorous treatment of the transport of heat and moisture within
the soil. Like in the big-leaf model a single isothermal surface layer is defined, but with
respect to evaporation a distinction is made between various surface fractions: open water,
vegetation, bare soil and snow1 (see Figure 4.1). This approach resembles the surface model
of Noilhan and Planton (1989).
The heat transport in the soil is parameterized by means of a diffusion scheme:
f \ ic dT _ d , 8T (4.9)
P h dt
where T is the soil temperature and XT the soil thermal conductivity. This equation is solved
using a fully implicit solution scheme and discretization of the soil volume in four layers, of
depth 0.07, 0.21, 0.72 and 1.89 m, respectively. The soil heat flux G is solved from the surface
energy balance (see below) and provides the upper boundary condition. At the bottom of
the simulation volume no heat flux is assumed to occur. Both p'Ch and XT are allowed to
vary with depth. p'Ch is formulated according to eq. 2.21, while Xr in layer i is paramete
rized according to Clapp and Homberger (1978) as function of the soil water content in that
layer, co,:
a 3z
f \
r3zJ
Since snow was not included in the data sets we use, it is not considered here
4. Selected models 1 11
hj =3-8 lv*tl -1/lnlO
rm yb/inio sat
CO;
(4.10)
co j, is the saturation moisture content, i p ^ is the saturated marrie potential and b the Clapp
and Homberger parameter. For very dry soils a minimum value is adopted for Xr. The
values of V|/Sflt, coSflt and b depend on the soil type, and are classified in 11 categories (Clapp
and Hornberger, 1978). As suggested by Mahrt and Pan (1984), the heat flux at layer
interfaces are computed with the "upstream" values for XT, that is, the highest conductivity
in either of the two adjacent layers, to minimize truncation errors associated with the profile
discretization.
skin layer
Figure 4.1: Schematic representation of the model of Viterbo and Beljaars (1995). For explanation, see text
zOm+1
t » ^ T . ' * * * M
rootzone »2 • • r 2
"3 • • T3
, •
Soil moisture transport is parameterized with a similar scheme, but here two
additional processes cause a change of the moisture content in a certain layer: free drainage
due to gravity, and root extraction by vegetation. The rate equation for soil moisture is given
by
112 Sparse canopy parameterizations for meteorological models
3co
IF a
'dz
, 3co Y
P A (4.11)
In this equation, pw is the density of liquid water, XH is the hydraulic diffusivity, yH the
hydraulic conductivity and Sœ the root extraction of water. In each layer, XH and yH are also
a function of water content, according to
yH = Y sat CO
CO sat
2b+3 (4.12)
and
*Y«tlV, saflfsatl C0„
CO
"sat
b+2 (4.13)
Again, a minimum value is adopted for both yH and XH, corresponding to the permanent
wilting point of the soil, co • The boundary conditions are provided by the infiltration of
rain minus the bare soil evaporation at the top, and a free drainage at the bottom (taking
3co/3z = 0).
The soil component of the model is coupled to the atmosphere by way of a so-called
skin layer, which has no heat capacity of its own. This skin layer represents the heat transfer
through the vegetation layer and loose organic material formed by litter or soil organisms.
The skin layer has a uniform temperature, Tsk. The soil heat flux is parameterized
empirically using an effective "conductivity", A:
G-AÇr^-TJ (4.14)
in which T3 is the temperature of the top soil layer. Tsk is solved similar to the big-leaf model
by considering the energy balance of the surface, which can be written as
(1 - a ) J T + (1 - E ) L 4 T 4
eaTsk = pc %k-%
P%<?sat(^)-%) + A ^ - T l ) ( 4-1 5 )
where xs and xl are resistance coefficients governed by the relative evaporation fractions of
the surface, and their corresponding water transfer resistances (in the original scheme of
VB95 the potential temperature at zR was approximated as Ta + g/c zR). The fraction of
vegetation cover, oy, is a surface dependent parameter. The fraction of the surface covered
with the skin reservoir, C;, depends on the amount of intercepted dew and precipitation by
the canopy leaves and soil surface. When snow may be ignored, the three evaporation
fractions are the open water skin reservoir (C;), the vegetation ((1 - C;) oy) and bare soil
((1 - C;) (1 - Or)). The resistance coefficients are simple weighted averages of the separate
resistances according to
4. Selected models 113
C, ( l - C , ) o , ( l - C , ) ( l - 0 / ) (4.16)
C, ( l -C ; ) oy a ( l - C ; ) ( l - o y ) (4.17)
where rsc is the canopy resistance, and a the relative humidity at the soil surface. The total
surface evaporation, E, is a weighted function of the evaporation rates from the skin
reservoir (E;), the canopy (£c) and the bare soil (Es):
(4.18) E = CIEl + (l-Cl)(afEc + (l-af)Es
In this formulation soil evaporation is treated using a so-called oc-type resistance
model (Kondo et al, 1990). Rather than regulating soil evaporation by use of an extra soil
evaporation resistance over the humidity gradient between the surface and the reference
level (ß-type resistance model), the relative humidity at the bare soil surface, a, is
parameterized. In VB95, a is a semi-empirical function of the soil content in the upper soil
layer:
a = i 0.5
1
1 -cos a>! < /cco/c
<»l>lc<ùfc
(4.19)
in which ac is a critical moisture content (in practice taken equal to the field capacity of the
soil, C0rc), and the factor lc (set to 1.6) accounts for the difference between the average
moisture content in the top soil layer and the moisture content near the surface. To avoid
excessive dewfall for dry soils during daytime, the humidity gradient aqsat(Tsk) - qa is
removed when 9saf(Ts)t) > qa and otqSflf(Tsjt) < qa (Blondin, 1991).
The fraction of the surface covered with the skin reservoir, C;, is determined by the
depth of the skin reservoir, wdew, given by
1,-dew
W„ (4.20)
where wmax depends on the leaf area index LAI» according to
H 'max= [<V M / . + ( 1 - ^ ] W iVMX (4.21)
Here, LAL refers to the leaf area per unit surface covered by vegetation, equal to LAI/<3c.
^MAX ' s t n e maximum amount of water that can be retained on a leaf surface. The rate-
equation for wdew is governed by the rate of evaporation from the skin reservoir (C;E;) and
114 Sparse canopy parameterizations for meteorological models
the interception, I, according to
dwdew I + ClEl ClEl I (4.22) dt Pw Pw Pw
The dew reservoir can evaporate very fast into the atmosphere, giving numerical difficulties.
A careful solution was proposed by VB95 in which the linear dependence of C; on wdew (eq.
4.20) is used. The interception of rain in the dew reservoir is calculated according to a simple
bucket scheme, taking the unfilled space of the dew reservoir and convecrive or large-scale
precipitation of rate P into account:
I = min r\ TE — J « m a x dew 025afT;p™—s—
(4.23)
The factor 0.25 accounts for the efficiency of interception of precipitation, and k is a
precipitation heterogeneity coefficient, equal to 0.5 for convecrive precipitation and 1 for
large scale precipitation. The remaining precipitation forms the throughfall rate, T, and is
available for infiltration into the soil, Is:
Is = T - £ s = P - 1 - Es (4.24)
where a reduction of soil infiltration due to soil evaporation is accounted for. Infiltration
rates exceeding the maximum uptake capacity of the top soil layer is added to run-off.
The aerodynamic exchange between the surface and the reference level is similar for
all surface fractions. VB95 assume an equal exchange for scalars and momentum between z0m
and zR, but allow for a lower surface roughness zoh for heat and scalars. The total
aerodynamic resistance, ra, appearing in eq. 4.15, is therefore given by eq. 4.4. ra can also be
expressed using the bulk transfer coefficient for heat, CH, according to
r; = - J - (4.25) CHua
where ua is the wind speed at reference height. CH was solved using the stability functions
*¥h of Beljaars and Holtslag (1991).
Finally, in VB95 the canopy resistance, rsc, is parameterized using a Jarvis-type model
(Jarvis, 1976) according to
r ^ ^ F j (PAR) F2(üJ) (4.26)
where rs m i n is a minimum stomatal resistance. The definition of LAL is equivalent to setting
r/(VB95) = oyrsc(big leaf) (see previous section). A dependence of rf on air humidity or air
temperature is not included. Dickinson et al. (1991) noted that there is no agreement among
modellers for the water stress dependence, and the available empirical evidence does not
allow for a general formulation. The functional dependence of rf on PAR is expressed as
4. Selected models 115 •
Fj(PAR) = 1 -fljln a2 + PAR
a3+PAR (4.27)
where av a2 and a3 are coefficients which may be related to canopy properties. PAR is
estimated by taking 0.55 K (1 - a). The dependence on soil humidity is similar to the
formulation proposed by Noilhan and Planton (1989), reading
F,(S)
CO - c o pwp
COr - CO fc pwp
CO < CO pwp
° V P < <° < °>fc (4.28)
"/c
In eq. 4.28 co is defined as
co = Rj C0j + R2 co2 + R3 co3 (4.29)
where R, is the relative root extraction in layer i. co~ and Sœ (eq. 4.11) are parameterized by
setting Rj = R2 = R3 = 1/3, thereby defining an effective rooting depth of 1 m.
Eq. 4.15 is solved by linearizing T^ using a Taylor expansion and qsat(Tsk) using a
value of dqmt/dT at the value of Tsk of the previous timestep. The ECMWF-scheme uses CH
from the previous time step explicitly, and an implicit solver for the temperature at the new
time level (Beljaars, 1992).
4.1.3 Impact of some simplifying assumptions in the new ECMWF-surface scheme2
Embedded in a global model, the new surface scheme presented by VB95 is designed
to describe the surface fluxes over a wide range of possible vegetation covers and time
scales. In order to avoid excessive data and computatial requirements, it is sometimes
necessary to simplify the parameterization of the transfer of scalars and momentum to and
from the surface.
One of the simplifications included in their scheme was the representation of the
surface by a single layer with uniform temperature. This layer is referred to as a 'skin layer'.
Four different grid box fractions with respect to evaporation are accounted for: bare soil, dry
vegetation, an open water skin reservoir filled with dew and intercepted water, and snow
(not treated here). The evaporation rate of each of these fractions is computed using a
humidity gradient between a reference level and the appropriate surface component (see
above).
In practice, the temperature of a non-uniformly vegetated surface can exhibit large
differences between e.g. the vegetation and the bare soil component of the surface. In
conditions of a well-irrigated vegetation stand only partially covering the surface and high
Adapted from Van den Hurk and Beljaars (1995)
116 Sparse canopy parameterizations for meteorological models
sensible heat release by the bare ground, adopting a single surface temperature for both the
vegetation and the bare ground can lead to a significant overestimation of the canopy
evaporation rate. Also, the predicted soil evaporation rate is often strongly overestimated for
a few hours after a period with rain, when canopy is also present. The temperature of the
canopy component rapidly increases once the intercepted water is evaporated, and this
temperature increase unrealistically enhances the simulated evaporation rate of the bare
ground.
A second simplification employed by VB95 is the use of an effective conductivity for
heat transfer through the skin layer. This skin conductivity, A (units W/m2K), defines the
temperature difference between the top soil layer and the skin layer, and accounts for the
heat flow into the soil component. A uniform value of 7 W / m K was chosen as to realize a
reasonable amplitude of the diurnal cycle of the ground heat flux, following Beljaars and
Betts (1992).
This section explores the consequence of these two simplifications for the sensible
and latent heat fluxes over partially vegetated regions. First, the original scheme is
compared to a slightly modified form, in which the temperatures are defined separately for
the relevant surface components. The performance and practical consequences of this
modification are evaluated using data collected during FIFE-1987 (Sellers et al., 1988) and
EFEDA-1991 (Bolle et al, 1993). Second, a suggestion for a physical interpretation for A is
made, and its value is evaluated experimentally. For this purpose, again EFEDA-1991 data are
considered.
• The skin layer temperature In order to avoid the unrealistic coupling between different surface fractions (e.g.,
bare soil and vegetation) through a single skin temperature, it is necessary to allow this skin
temperature to be different for the bare soil, the vegetation and wet surface fractions. Once
the vegetation temperature is allowed to differ from the bare ground temperature, excessive
canopy evaporation under dry conditions is readily avoided. In practice, vegetation can
remain much cooler than bare ground, because it can sustain evaporation by accessing water
from deeper soil layers. Multiple source models, as presented for instance by Dolman (1993),
allow for these temperature differences by using the Penman-Monteith concept (Monteith,
1981) separately for the canopy elements and the underlying soil.
The scheme of VB95 solves the skin temperature Tsk implicitly by considering the
energy balance of the surface (eq. 4.15), in which the soil heat flux G is given by eq. 4.14. The
total sensible and latent heat fluxes H and XE can be deduced from eq. 4.15 and are specified
according to
H--PCHua{cpTsk-cpTa-gzR) (4.30)
and
XE=Xp(Xsc,sat(Tsk)-xfla) ( « I )
where the original formulation is used for the potential temperature at zR.
4. Selected models 1 1 ' B
Obviously, the values for T$k found from eqs. 4.15,4.30 and 4.31 will depend on the
relative surface fractions covering the grid box. When the crop resistance differs from 0 and
the relative humidity at the soil surface < 1, Tsk will depend on C; and oy. For instance, with
C; = 1 the entire grid box has a wet skin reservoir, and the skin temperature will adjust to a
potential evaporation rate (rf -» 0, a -> 1). In cases where C; = 0 and oy = 1 (vegetation only)
the skin temperature will be lower than when oy = 0 (bare ground only), owing to the larger
evaporation capacity of vegetation.
A straightforward strategy to compute the temperatures of the different surface
fractions is to solve eq. 4.15 separately for each component, by choosing appropriate values
for %i and xs. The final grid box averaged energy flux is then computed from the energy
fluxes and temperatures from each component according to the same weighting scheme as
presented in eq. 4.18. A similar strategy is adopted in the "tile"-approach by Koster and
Suarez (1992), albeit that in their model the energy balance in each tile is solved by using a
simplified form of the two-component model SlB (Sellers et ah, 1986).
For practical applications two issues need further attention: the stability dependence
of CH, and the solution of the surface temperature from the linearization around the
previous timestep.
An important issue is the treatment of the aerodynamic resistance between the
surface and the lowest atmospheric grid point, rfl = l/CHua. Since the value of CH depends
on atmospheric stability — and therefore on the sensible heat flux — its value is expected to
be different for the separate surface fractions when local energy balances differ. In the VB95
model the transfer from the different surface fractions is computed independently, using a
uniform value of CH for all fractions. The independent treatment of surface fractions is
reasonable if the surface fractions are large enough to have internal boundary layers that do
not merge below the lowest model level. For patchy surfaces with small horizontal scales, it
would be necessary to introduce an extra node in the resistance network somewhere
between the surface and the lowest model level (Blyth, 1995), but such a concept is difficult
to handle in a global model without appropriate data sets.
In line with VB95 it would be appropriate to parameterize the transfer coefficient CH
separately for each surface fraction. In that context, the stability correction in CH for each
fraction is dependent on its exchange of sensible heat with the reference level. If additional
storage of parameters between subsequent time steps should be avoided, the value of CH
can no longer be estimated from the previous time step, and for each fraction the energy
balance should be solved iteratively in order to determine CH. However, in general the
stability functions in CH are relatively unimportant in the parameterization of sensible and
latent heat exchange between the surface and the atmosphere, and therefore a first
approximation may be sufficient. The dependence of CH on atmospheric stability can be
expressed using an average sensible heat flux, which is obtained from the separate energy
balance solutions and a weighting scheme defined by eq. 4.18. A major practical advantage
is, that we can proceed deriving CH from the previous time step and avoid iterations for
determination of the surface temperature and the surface energy balance for each surface
component.
When the temperatures of the individual surface components show significant
differences (as can be the case for a sparsely vegetated surface with evaporation from
• 118 Sparse canopy parameterizations for meteorological models
plants), the linearization of dqml/dT at a (weighed) average value of Tsk from the previous
timestep can introduce significant errors. Obviously, similar errors are introduced if a
linearization around the reference temperature is carried out and the surface temperature
differs significantly from this value (McArthur, 1990). The error can be minimized by storing
all three surface temperatures separately rather than a weighed average between two
subsequent time steps. Alternatively, for each component the surface temperature can be
initialized with the weighed average from the previous time step, and a (small) number of
iterations is needed in order to update dq^/dT and to find the actual value of the surface
humidity. The number of iterations will depend on the actual temperature differences, but
generally can be limited to 2 or 3.
In the following we will demonstrate the implication of solving separate surface
temperatures by adopting two iterations to solve the surface energy balance and find its
temperature. The calculations are initialized using the average sensible heat flux and surface
temperature from the previous time step, as is currently applied in the ECMWF surface
scheme. In a subsequent section this numerical strategy will be compared to a fully iterative
approach for solving the surface energy balance.
• Case studies for the temperature differentiation Two case studies demonstrate the effect of discerning between the different grid box
fraction temperatures: a case regarding a drying surface after rain (measurements from FIFE),
and the simulation of a series of diurnal courses of the evaporation of a sparse vineyard
canopy surface (measurements taken during EFEDA).
Table 4.1: Surface parameters for the FIFE-1987 test case
parameter symbol value
roughness length for momentum
roughness length for heat
surface fraction covered with vegetation
surface albedo
longwave emissivity
initial soil temperature
initial soil humidity
z0m
z0h
°l a
£
T
CO
0.3 m
0.03 m
0.85
0.168
0.996
291.4 K
field capacity
A drying surface after rain
The original model of VB95 was validated with several data sets, including the data
collected during the FIFE-1987 experiment (Sellers et ah, 1988). During this experiment
micrometeorological parameters were measured during 168 days, from May until October
1987. Data were collected above a tallgrass prairie in rolling terrain. Half hourly averages of
temperature, wind speed and air humidity at reference height, as well as incoming
longwave and shortwave radiation are available. During four intensive field campaigns
(iFC's) eddy correlation data of sensible and latent heat flux density were collected, together
with net radiation and soil heat flux density. The observations from all available stations
4. Selected models 119
were averaged to obtain a single time series by Betts and Ball (1992).
Both the original and the modified scheme were used to simulate the surface fluxes
for the entire experimental period. All model settings (including soil type and root profile)
were taken as in the original paper. Values of some surface specific parameters can be found
in Table 4.1. The soil moisture profile was initialized at field capacity, and a vertically
uniform temperature profile was taken as initial profile.
For comparison with measured fluxes, a situation is selected in which the surface is
drying after a period of rain. For the present study the simulations for days 176 and 177 are
chosen. Unlike the intercomparisons in VB95, we focus on diurnal variations of measured
and predicted surface fluxes.
Figure 4.2: (Lower panel:) Observed (•) and simulated (heavy lines) total evaporation for FIFE-1987, days 176 and 177. Simulations are carried out with both the original VB95 model (••••) and the new version with different temperatures for different surface fractions ( ). Also shown are the simulated evaporation from the skin reservoir, Cj A.E( (thin lines) and observed precipitation (upper t
700
176.5 177 day in 1987
177.5 178
Figure 4.2 shows the simulated and observed total evaporation for the selected days.
Also precipitation is shown, and the calculated evaporation from the skin-reservoir, A.E;. The
new scheme reduces the overestimation of A.E by approximately 50%, especially for day 176.
Also the pronounced peaks caused by the skin evaporation are reduced, although not
entirely removed. As was discussed by VB95, the skin reservoir is very shallow (< 0.7 mm),
and can fill up and evaporate within a single time step. However, in their scheme the value
of C; is computed from the skin reservoir content in the previous time step. The result is that
skin evaporation does not take place during the first time step of filling the reservoir by
interception. Too large time steps can result in simulation of a excessive peak transpiration.
The choice of the fairly large timestep used here (1800 s; equivalent to the time step in the
120 Sparse canopy parameterizations for meteorological models
ECMWF model) causes the remaining part of the overestimation of the evaporation, visible in
Figure 4.2.
The new solution for the surface temperature has a pronounced effect on the
partitioning of the evaporation over the ground surface and the canopy. Figure 4.3 shows
the simulated bare soil and canopy evaporation rates, given by (1 - C;) (1 - oy) XES and
(1 - C;) Or XEC, respectively. Since the soil is wet just after a rainy period, the bare soil
evaporates at a nearly potential rate, which has a strong feedback to the surface
temperature. The old scheme simulates a maximum weighted soil evaporation of about 300
W/m 2 . For the bare ground fraction (equal to 15% when C; = 0), this is equivalent to 2000
W/m2! The reason is that the dominating vegetated part enforces its higher surface
equilibrium temperature on the bare soil fraction. Allowing for different temperatures of the
soil and the canopy component causes a reduction of 50% of the soil evaporation, whereas
the canopy evaporation is enhanced by approximately 10% around noon.
500
176.5 177 177.5 day in 1987
Figure 4.3: Simulation of the canopy evaporation, (1 - C,) oy XEC (thick lines) and soil evaporation, (1 - c() (1 - oy) A,£s (thin lines) for the original model ( ) and new
version ( )
A sparsely vegetated vineyard
The model of VB95 was also run for a sparsely vegetated Mediterranean vineyard
area for five consecutive days in June 1991. Data were collected in the Tomelloso area during
the EFEDA-I intensive measurement campaign (Bolle et al, 1993). The fraction of area covered
by vegetation was about 12% in the considered period, and the Leaf Area Index did not
exceed 0.3 m 2 /m 2 . Since dew and precipitation were absent in this period, the fraction of
area covered by the skin reservoir (C;) was zero all time. The soil consisted of sandy loam
material and the top layer was covered with stones and very dry. The plants extracted water
from deeper soil layers (> 1 m), and canopy evaporation could be sustained in spite of the
very dry top soil.
Energy balance measurements were obtained as indicated in section 2.4.3. Surface
temperatures were obtained from an infrared sensor moving along the cable at 3 m height
4. Selected models 121
(section 2.2.3). The crop resistance rf was inferred from measured values of total
evaporation and canopy temperature. Evaporation from the underlying soil was assumed
zero, and aerodynamic resistances in the pathway between the canopy and the reference
height were parameterized according to Choudhury and Monteith (1988). Sene (1994)
showed that the final value of rf is not sensitive to the exact values of these aerodynamic
resistances. More details about the experimental setup can be found in section 2.2.
For the settings of most model parameters the suggestions made by VB95 were
followed. The original treatment of the crop resistance (eqs. 4.26 - 4.28) was replaced by the
formulation of Choudhury and Monteith (1988), calibrated to match the current data (see
Figure 4.4). The physical soil parameters were quantified according to the sandy loam soil
type cited by Noilhan and Planton (1989). Surface albedo was taken 0.29 at all times,
obtained from field observations. The apparent conductivity of the skin layer (A) was taken
7 W/m2K, and the drag coefficient CH was computed using z0m/zoh = 200, following Van
den Hurk et al. (1995). These adaptations were necessary to predict a reasonable value of the
surface temperature and the soil heat flux.
10000:
I 1000:
173 174 doy(1991)
Figure 4.4: Values of the crop resistance for 5 days during EFEDA-91; »: data inferred from measured total evaporation; predictions using a calibrated model of Choudhury and Monteith (1988)
Figure 4.5 shows observations and simulations with the original scheme of bare soil
temperature (4.5A), plant temperature (4.5B) and total latent heat flux (4.5C). Simulations
with both the original and the modified scheme are shown. For the original model, the
simulated temperatures of the canopy and the bare soil are represented by the average skin
temperature.
The total soil heat flux and average surface temperature are hardly affected by the
new parameterization (figures not shown). The surface temperature is dominated by the
bare ground component, since the area fraction of vegetation was very limited (Figure 4.5A).
However, the impact of the new temperature scheme on the total evaporation rate (4.5C) is
significant, and a reduction of almost 50% is caused by adopting the new scheme. The
reduction of the evaporation is balanced by a slight increase of the sensible heat flux,
consistent with a closed surface energy balance.
122 Sparse canopy parameterizations for meteorological models
340-
Figure 4.5: (A) Bare soil temperature, (B) canopy temperature and (C) total latent heat flux for the EFEDA-91 case. Shown are observations (») and model simulations with the original (•••••) and new ( ) formulation
340-
330-
320-
^ 3 1 0 -
§ 300-1-
290
280
270
B
fA
M N j r \
ft i 1
1
im!
A fi M L ta, 'û
, fXM \f ¥ 173 176
day
E/fecf of the numerical scheme on the energy balance solution
During the second (EFEDA) case, occasions with high sensible heat fluxes and surface
temperatures often occurred. Therefore this is a good case to demonstrate the effect of
4. Selected models 123
numerical approximations of CH, as outlined previously. We confined ourselves to the
modified scheme, in which the surface temperatures are solved separately for each
surfacefraction. Three strategies are compared:
(1) as applied above, that is, computing CH by use of an average sensible heat flux from
the previous time step, and solve the energy balance of each surface fraction by
means of 2 iteration rounds
(2) same procedure, but with only a single iteration round, and
(3) same procedure, with iterations until convergence.
A: Total evaporation B: Total sensible heat
40 60 80 iterative scheme
350i
300
„ 2 5 0
I | 200
§ 1S0' | i o o
I 50 X
-50
-100
A
JHttTr'
AAAk*-JS
^Ifcfi*
50 100 150 200 250 iterative scheme
C: Aerodynamic resistance for heat D: Skin temperature
300 310 320 iterative scheme
Figure 4.6: EFEDA-1991 simulations of (A) total evaporation, (B) total sensible heat flux, (C) aerodynamic resistance and (D) average skin temperature, computed by means of a fully iterative scheme for each surface fraction (x-axis), and an explicit correction of ra for stability effect using sensible heat fluxes from the previous time step, with 1 (») and 2 (°) iterations (y-axis)
Figure 4.6 shows the results in terms of simulated total evaporation (4.6A), total
sensible heat (4.6B), aerodynamic resistance ra (4.6C) and bare soil temperature (4.6D). A
clear difference is present between procedures (1) and (2) for especially the simulated latent
heat flux. Ignoring the error involved with the linearization of dqsat/dT (procedure (2))
results in serious deviations compared to the fully iterative scheme (3). The deviations are
particularly large for relatively low values of XE, which occur just after sunrise and before
sunset when the rate of change of the surface temperature is large. Smaller deviations are
124 Sparse canopy parameterizations for meteorological models
present for the sensible heat and bare soil temperature.
It is also evident from Figure 4.6 that a significant reduction of the deviation between
an iterative and an explicit formulation is obtained by allowing for an extra iteration round
(procedure (1)). The total evaporation, sensible heat and bare soil temperature agree now
very well with the iterative approach. The aerodynamic resistance computed using CH from
the previous time step differs from the iterative solution for only a small number of high
values of ra, which occur under stably stratified conditions with small sensible heat fluxes.
The large deviations shown in Figure 4.6C (on a logarithmic scale) are not found in the plots
for sensible heat and bare soil temperature. The parameterization of the turbulent fluxes
appears to be rather insensitive to the way stability effects are incorporated in CH.
• The numerical value of the skin conductivity In the model of VB95, the apparent skin conductivity, A, is defined as the heat flux
through the vegetation layer per degree temperature difference between the skin layer and
the upper soil layer (see eq. 4.14). For calculations on the global scale, VB95 treat A as a fixed
coefficient, with a value of 7 W/m2K (Beljaars and Betts, 1992). However, considerably
different values may be expected for different types of surfaces.
For densely vegetated canopies, the value of A includes the heat conductivity of the
canopy elements, the air within the canopy layer, and the top soil layer. Complicated
processes like aerodynamic transport within the canopy layer and heat conduction through
the stems inhibit an easy quantitative assessment of A. However, since the presence of the
vegetation will insulate the soil thermally from the atmosphere, A may be expected to be
small.
On the other hand, when vegetation is sparse or absent, the skin temperature is
dominated by the (underlying) soil. In that case, the temperature difference appearing in eq.
4.14 is proportional to the soil temperature gradient immediately below the surface, which
may be significant, especially for dry soils. Eq. 4.14 can be compared to an ordinary
conductivity equation for soil heat flow, of the form
AT ö . 3T
"Äz Tlz -A AT = -(A Az) 4 - - -34.4- ( 4 3 2 )
where AT is equal to T2 - Tsk. From this equation, the apparent heat conductivity A can be
interpreted as a physical conductivity by multiplication with a reference depth. The
temperature difference defined by eq. 4.14 can be treated as a real gradient through division
by the same depth. Thus, for bare soils A Az is proportional to the soil thermal conductivity
XT, which depends on type and moisture content of the top soil.
A similar approach was followed by Mahrt and Pan (1984), who chose Az to be the
centre of the model top soil layer, that is, Zj/2. In cases of steep non-linear temperature
gradients near the surface, significant truncation errors are introduced when Zj is chosen too
large. Therefore, a better choice for Az would be the depth where the real temperature
profile equals the temperature of the model top soil layer, Tj. In principal this will not be a
constant depth. At times where the soil heat flux density is large, steep temperature profiles
with an exponential shape are present, and Az is expected to be closer to the surface than
Zl/2.
4. Selected models 125 •
The EFEDA-dataset, described above, provides a useful test-case to determine a value
for A for a typical Mediterranean sparse canopy surface. Simulations of soil heat flux density
were carried out using VB95, in which soil physical and aerodynamic parameters were
selected as before. In order to examine the effects of the choice for A in the present ECMWF-
scheme, sensitivity experiments were carried out with three different values of A, namely 7,
14 and 20 W/m2K.
Figure 4.7 shows the simulated and measured soil heat flux G for the 5 consecutive
days in June 1991. Clearly, the default value of 7 W/m2K yields an underestimation of G of
approximately 60% at all times. A = 20 W/m2K gives an optimal simulation. The
intermediate value of 14 W/m2K results in only a slight underestimation of G (<20%, on the
average). As a consequence of the surface energy balance equation the sensible and latent
heat fluxes are reduced by several tens of W/m 2 at most when A is increased from 7 to 20
W/m 2 .
250
173 174 day (1991)
176
Figure 4.7: Measured (») and simulated (lines) values of the soil heat flux for the EFEDA-1991 case. Simulations include A = 7 (—••), 14 (- - - ) and 20 ( ) W/m 2 K
Also shown are the simulated temperatures of the skin layer and the first soil layer
obtained using A = 7 and 20 W/m2K (Figures 4.8A and 4.8B, respectively). Observations of
the temperature of the upper soil layer were derived by an arithmetic average of the
temperatures at z = 0.03 and z = 0.05 m. The effect of A on the skin temperature is only
moderate. The skin temperature is a key parameter in the entire energy balance solution (eq.
4.15), and is only to a small extent determined by the heat flow into the soil. The prediction
of the temperature of the first soil layer, however, is much improved when A = 20 W/m2K is
used.
• Discussion and conclusions
This section considers two types of simplifications applied in the new ECMWF surface
scheme: a uniform skin layer temperature, and a constant value of the skin layer
conductivity for all surface types.
A simple scheme is presented to allow the different surface fractions (bare soil, dry
vegetation and a skin reservoir of intercepted water) to adopt temperatures that are in
126 Sparse canopy parameterizations for meteorological models
equilibrium with their state of evaporation, as in the Penman-Monteith concept (Monteith,
1965). The three surface temperatures are solved according to the original scheme by first
regarding each of the fractions as if fully covering the grid box, and then average the
resulting fluxes and surface temperatures using a similar weighting as used for the
evaporation (eq. 4.18). By initializing each surface fraction energy balance solution using the
average skin temperature from the previous time step, and employing a second iteration to
minimize the error involved with linearization of dq^/dT, no additional information needs
to be stored between subsequent time steps. This numerical scheme is shown to have
virtually identical results as a full iteration for each surface fraction energy balance.
173 174 day(1991)
330
320
310-
g
300
290
280
B
it \t
\
I 1 V i i y ¥
i
i k [1 1 1 1 \ \
kk \i\ J \M ty
173 174 day (1991)
Figure 4.8: Observed (*) and simulated (lines) values of (A) the skin temperature, and (B) temperature of the top soil layer. Simulations include A = 7 ( ) and 20 ( ) W/m2K
This procedure is somewhat different from the dual source models presented by e.g.
Deardorff (1978), Shuttleworth and Wallace (1985) or Choudhury and Monteith (1988). In
their models, an interaction between the bare soil and vegetation takes place directly by
computing a temperature and humidity deficit within the canopy layer, and computing
fluxes from either of these components through this canopy layer node. Blyth (1995)
presented a more general concept by placing this node at some level between the surface
and the lowest model layer, which serves as a reference height for the surface forcings.
A major disadvantage of this concept for large scale meteorological models is the
data requirement. The values of the resistances between this node and the various surface
fractions need to be parameterized, and cannot be expected to be of similar magnitude for
all vegetation types or degrees of coverage (McNaughton and Van den Hurk, 1995). In the
current ECMWF-scheme the aerodynamic transfer between the surface and the reference level
allows no direct interaction between various surface fractions, since the fluxes from each
component are treated as purely additive. However, in a surface layer model coupled to a
model for the rest of the atmosphere, the surface fluxes will affect the meteorological
forcings at the reference height via boundary layer interaction. This feedback serves as an
indirect interaction mechanism between the surface fractions.
In the original scheme, the computation of the surface evaporation (eq. 4.18) is
4. Selected models 127
conceptually almost3 similar to defining a single surface resistance for evaporation,
weighted by the various grid box fractions (see eqs. 4.16 and 4.17). Based on numerical
simulations over heterogeneous terrain, Blyth et al. (1993) argue that an average resistance
defined in this way will underestimate an effective surface resistance, which is defined by the
ratio of the humidity gradient to the average flux in the grid box. This effective resistance
should be obtained by weighting the surface resistances in a grid box by the various fluxes
rather than by the grid box fractions. In the new scheme, however, the effective resistance is
no longer solely determined by the grid box fractions, but takes differences between
humidity gradients of the various fractions also into account. By definition, a single surface
resistance yielding the same average flux is now equal to the effective resistance, weighted
by the fluxes from the various grid box fractions. Obviously, this is only applicable to the
fractions which are actually considered in the surface model: the influence of a variability of
different crop resistances for patches of different vegetation types within a grid box (Koster
and Suarez, 1992) is only implicitly included in the parameterization of /•ƒ present in VB95.
In a case study where the behaviour of a drying vegetated surface wetted by rain
was simulated, the new scheme considerably altered the partitioning of latent heat flux over
the vegetation and the soil. In the original scheme maximum soil evaporation was of the
same order as the canopy evaporation, in spite of the fact that only 15% of the surface was
not vegetated. The new scheme reduced the soil evaporation by 50%, and enhanced the
canopy evaporation slightly.
A case study carried out using a dataset collected over a sparsely vegetated dry
vineyard with negligible soil evaporation showed a significant reduction of the canopy
evaporation. The simulations of total evaporation carried out with the new scheme matched
observations rather well, while the original scheme caused an overestimation of
approximately 100%. Obviously, a similar change of the simulated canopy evaporation
could also be forced by changing the value of the surface resistance, rf. However, it merely
is the purpose of this demonstration to show the effect of the assumption of the uniform
surface temperature used by VB95, rather than to verify all components of their model. The
present case shows this assumption to have a significant impact on the canopy evaporation
rate.
In general, solution of the surface temperature for separate surface components
reduces evaporation of those components which are cooler than their surroundings. In the
FlFE-dataset, the soil evaporation was significantly reduced, whereas evaporation by the
vegetation was reduced for the Spanish simulation.
Also the parameterization of the soil heat flux by use of a skin conductivity A,
assumed constant for all vegetation types, was evaluated using data collected during EFEDA-
1991. It was shown that for the limit of a bare soil surface, A is proportional to the soil
thermal conductivity XT. The coefficient of proportionality is a reference depth Az. Mahrt
and Pan (1984) proposed to choose Az as the centre of the top soil layer, but for steep non
linear temperature gradients this depth may be chosen closer to the surface.
For the dry Mediterranean vineyard, soil temperature and soil heat flux data showed
A deviation from this concept is caused by treating the evaporation from the bare soil component using the relative humidity a, rather than defining a soil evaporation resistance
128 Sparse canopy paramelerizations for meteorological models
that A = 20 W / m K is a better estimate than the presumed value of 7 W / m K . For this case,
the thermal conductivity of the upper soil levels was estimated at 0.3 W/mK (Verhoef et al,
1995). Using A = 20 W/m2K, Az would be approximately 1.5 cm.
The value of A = 7 W / m K was obtained from soil heat flux densities observed at a
meadow grass land site near Cabauw, The Netherlands (Beljaars and Berts, 1992). The
difference with the value found from the EFEDA-1991 data is presumably associated with the
different insulation properties of the vegetation types at both sites. Whilst the sparse
vineyard canopy had a low degree of vegetation cover (-12%) hardly providing a barrier for
heat transfer between the soil and the atmosphere, the grass vegetation near Cabauw more
effectively insulated the underlying soil. These two values found for A possibly mark the
likely range of values for most surface types. Including experimental evidence for tall
vegetations (forests) or completely bare surfaces (deserts) might further extend this range.
However, in order to limit the global input requirement, a simple differentiation between
the two values of A — preferably based on grid box vegetation cover — would provide a
significant improvement of current parameterizations.
For surface flux predictions at seasonal or even annual time scales, the exact
determination of the soil heat flux is not too crucial. The diurnal average soil heat flux is
generally small compared to the total net radiative energy supply. However, the diurnal
course of G affects the predicted diurnal latent and sensible heat flux patterns. For various
applications these diurnal patterns have a considerable impact (e.g., prediction of
temperature at screen height, timing of development of convective clouds, studies of
atmosphere-surface feedback processes etc.), and a correct estimate of G may be significant.
4.1.4 The two-layer model of Deardorff
Unlike the surface schemes discussed above, the surface model of Deardorff (1978,
referred to as D78) treats sensible and latent heat fluxes separately for the vegetation
elements and the underlying soil. It was one of the first two-layer models, presented in a
paper actually comparing various parameterizations of surface temperature related to soil
heat flux density. Deardorff's model is the base of the Biosphere-Atmosphere Transfer
Scheme (BATS), developed by Dickinson et al. (1986,1993) for application in GCM's. In the
version included here a few minor parameterizations were replaced as recommended by
Dickinson et al. (1986). A schematic lay-out of Deardorff's model is shown in Figure 4.9.
The basic concept of D78 consists of a solution of the energy balance of the canopy
elements and the soil surface separately. Ignoring heat storage in the vegetation and energy
consumption by photosynthesis, the canopy energy balance is given by
*!-lt+li-LÏ-He.*Ee <4.33)
At the soil surface the energy balance is
Kt-Kl+Lt-L:=HS+XES+G (4.34)
In eqs. 4.33 and 4.34 the subscripts c and s denote canopy and soil fluxes, respectively.
The partitioning of net radiation over the canopy and the soil surface is specified by
4. Selected models 129 •
use of a vegetation coverage factor oy. Unlike the later two-component models (see next
section), D78 does not entirely rely on a solution of the Penman-Monteith equation, but on a
direct solution of the surface flux equations by using prognostic equations for the surface
temperature and humidity. This prognostic equation is derived from the force-restore
method for the temperature and humidity of the soil surface.
Canopy
Figure 4.9: Schematic layout of the model of Deardorff (1978). For explanation of symbols: see text
Soil surface
root zone .
EZKZh-f To
Ts • "Qs
force-restore
T2
z0m + d
Incoming shortwave radiation is distributed over the canopy and soil proportional to
oy, according to
I 1 Kc = ofK
l
Kls = (l-of)K
l (4.35)
The canopy is not transparent to shortwave radiation. The reflected shortwave radiation is
calculated using a separate canopy and ground albedo, ac and as:
T i
K -*cKc Î 1
Ks = «sKs
(4.36)
Net longwave radiation of each component is determined by the atmospheric emission
(distributed similarly as for shortwave radiation) and longwave exchange between the
canopy and soil. The canopy emits longwave radiation upwards and downwards, and
absorbs radiation emitted by the atmosphere and the ground:
T 1 C S E L + OT:
e + 2 E . ee„
e +£ - 2 E E c (4.37)
in which the same subscript conventions apply as before. The longwave radiation
components at the ground surface are given by
130 Sparse canopy parameterizations for meteorological models
i l M „ w ^ „ ecoTc4 + ( l - e c ) e s 0T s
4
7 7 e„ + e - e„ e„ (4.38)
LsT = (i-cy)
.4 ,„ „ „,4
e^rSd-e , )^ + o, e,org+(l-es)ecorc (439)
7"
These relatively complicated equations simulate the longwave radiation exchange between
two parallel plates, representing the canopy and the soil surface.
The transfer of heat and water vapour from each of the two surface components
takes place via a common node in the resistance network (see Figure 4.9), representing the
temperature and specific humidity of the air within the canopy layer, 0O and q0 respectively.
Here, a potential rather than an actual temperature is used. Since 60 and q0 are affected by
fluxes from both the soil surface and the canopy, a direct interaction between these two
sources is allowed. The aerodynamic exchange of heat between the canopy elements and the
canopy air is parameterized as
e c - e 0
ra
where Tb is a factor accounting for sensible heat exchange from non-evaporating parts. The
sensible heat exchange from the soil surface is given by
Hs=pcp^-1 (4.41) r„
Here, the transfer coefficient formulations in D78 are expressed as a resistance formulation,
comparable to the resistances in the other two-layer models. An equivalent formulation is
used for the exchange of water vapour from the soil surface, written as
Es - p ! l ^ l (4.42)
The specific humidity at the soil surface, qs, is treated similarly to VB95, that is, by expressing
a surface relative humidity as a function of the soil moisture content of the top soil layer. In
D78 the factor / appearing in eq. 4.19 to account for humidity gradients in the top soil layer,
is set to unity.
The water vapour flux from the canopy is formulated somewhat differently, since it
accounts for the evaporation from both intercepted water and from the canopy leaves.
Analogous to eq. 4.42, a potential evaporation, Efot, is first defined as
4. Selected models 131
-.pot = p
1c-% (4.43)
where qc = q^ÇT^. The actual canopy evaporation, Ec, is a fraction Ç of Ef'. 't, depends on
the stomatal resistance rst, the leaf boundary layer resistance rb and the relative amount of
intercepted water, wdew/wmax, given by
% = 1 - 5 w. dew
2/3 (4.44)
where 6 = 0 when condensation is occuring (q0 > qc) and unity otherwise. Unlike in VB95, a
power function is used to express a higher dew evaporation rate when the dew reservoir
gets empty, which in practice correponds to the formation of droplets on leaves with a large
surface area. Combination of eqs. 4.43 and 4.44 yields the total canopy evaporation, Ec:
\K pot (4.45)
Only the transpiration by the leaves, Et, is extracted from the soil water reservoir (see
below), and is specified as
Et = 5 -.pot
rst + h l - dew
2/3
w v m a xv
(4.46)
The canopy sensible and latent heat exchange are determined by an iterative solution
of the canopy temperature, 6C. A Newton-Raphson iteration scheme is used to solve Tc and
6C from eqs. 4.37 - 4.45, for specified values of 90, q0, Ts and radiative input.
The temperature at the soil surface, 9S, is calculated by use of the force-restore
method (Bhumralkar, 1975). The absolute surface temperature, T, is determined by a forcing
heat supply from the surface (G) and a restoring thermal diffusion from below, depending
on the temperature of the lowest slab, T2:
*Ts _ 2ftG 2n(Ts-T2)
dt K4 (4.47)
t j is the length of the diurnal wave (24 hrs). d1 is equal to the depth of the diurnal
temperature wave, and depends on the thermal diffusivity and volumetric heat content of
the soil. Gradients of these thermal properties may be induced by a variation of soil
moisture content with depth. Following Deardorff (1978), these gradients are accounted for
by application of an empirical weighting over the two soil layers:
132 Sparse canopy parameterizations for meteorological models
P'Ch<*l)s - ' • f (p / c j 1 ^7 l + (l -r'%'ci)jk^[ (4.48)
where r' is a coefficient equal to 0.30 + O.OSCÛJ/O^, and kt is the thermal diffusivity (equal to
XT/p'Ch) in layer i. T2 can be estimated using the e-folding depth of the annual temperature
wave, d2:
dT2
IF ?'Cl±
(4.49)
with d2 given by J ^ - ^ an<^ T2 = ^65 t j . The force-restore method is based on the solution of the surface temperature for a
periodic surface forcing, assuming that the thermal properties of the soil are constant with
depth. Dickinson (1988) derived slightly modified force-restore expressions for a surface
forcing which consists of higher harmonics (induced by for instance shading by clouds or
surface elements). However, as he pointed out, the impact of the higher harmonics on the
surface temperature is quickly damped, and can be ignored in most cases. He also
considered non-homogeneous soils, of which soils covered with layers of snow or litter are
extreme examples. Although the implications of this heterogeneity for a proper solution for
Ts may be significant, these modifications are not considered here.
The soil moisture content of the top soil layer is also described using a force-restore
parameterization, calibrated for various soil types by Noilhan and Planton (1989). The
surface forcing is formed by the balance between the surface precipitation rate, Ps (given by
(1 - oy)P), soil evaporation, Es, and a fraction R3 of the total canopy transpiration, Et. The rate
of change of the soil moisture content in the top layer is given by
dco-, C, i = — P •
dt p z, \ s •Wt)
C2((o1 %») (4.50)
The depth of the upper slab, z1 w, is an arbitrary normalization depth, set to 0.1 m. Deardorff
(1978) chose R2 = 0.1, but we follow Noilhan and Planton (1989), ignoring transpiration
extraction from the top layer. Cj and C2 are soil type specific coefficients depending on soil
moisture content, porosity and isothermal water vapour transport. The coefficient Cj is
specified as
2z, "l,œ
nc„ Mffli)
K^aj) (4.51a)
while C2 is expressed using a calibration coefficient C2rer depending on soil type as
4. Selected models 133
C2 " C2ref CO.,
(4.51b)
in which cw is the hydraulic capacity (equal to 9o)/3v|/)/ KT the isothermal water vapour
diffusivity and CO; a small numerical value to limit C2 at saturation. KT is estimated as
Dv8esat(Ts) /Vj- — xp
P-esatWs) (RvTf CO, OJj) (4.52)
with Dv the molecular diffusivity of water vapour, x = 0.66 a tortuosity factor, and Rv the
gas constant for water vapour (Braud et al., 1993). The value of C-, is limited to the value at
CÛS = co^. Noilhan and Planton (1989) give a simplified equation for Cv in which isothermal
water vapour diffusion is not included. In the current study, eq. 4.51a is used for Cj instead.
An equilibrium lower soil moisture content, co , replaces co2 in eq. 4.50, to account
for gravity effects, co is defined as
( N I
CO eau
CO, - C O sal eau
CO,
Cûc
( 1 -
C0o y*p,
co„
equ (4.53)
In eq. 4.53 a and p are calibration coefficients, determined for various soil categories by
Noilhan and Planton (1989).
The time dependent equation for the soil water content in the lowest soil layer is
written as
3co2 i i = : IF
Pwz: w^l.w • E < )
(4.54)
z2 w is the depth of the bulk soil moisture reservoir, and must be specified explicitly.
The depth of the dew reservoir, wiew, is determined as function of the intercepted
precipitation, the collection of dew and the evaporation from the dew reservoir. Interception
J is assumed to be equal to the precipitation falling on the part of the surface covered by
canopy elements. wdew thus changes according to
dw dew
dt afP •{Ec-Et) 0 < Wj < w
dew max
(4.55)
where wmax remains to be specified. Dew water collection exceeding the maximum reservoir
depth is added to the soil precipitation rate, Ps-
Originally, D78 obtained G0 as a weighted average of the temperatures at the
reference level, 0fl, of the canopy, 9C and of the bare soil surface, 6S. The weighting factors
were assumed to be fixed. A value of q0 was obtained similarly. Dickinson et al. (1986)
replaced this formulation by a weighting over the resistances connected by the node within
the canopy:
134 Sparse canopy parameterizations for meteorological models
iAa" + tyr; + i/r;
e = , ' « t e ' « s' a ( 4 - 5 6 )
The aerodynamic resistance above the canopy, rfla, is expressed using the bulk
transfer functions of Louis (1979). By choosing the roughness length for momentum, z0m, to
coincide with the within-canopy resistance node, the solution of ra" is similar to eq. 4.5. The
excess resistance in the one-layer models formally corresponds to a combination of the extra
resistances rac and ra
s in the two-layer models (see figure 4.9). D78 describes the bulk
boundary layer resistance, rac, equivalent to a leaf boundary resistance according to
LAI LAI omfjfu
(4.57)
where lw is a characteristic leaf dimension. Eq. 4.57 is derived from Nusselt number scaling
arguments, accounting for the difference between momentum and heat transfer. The value
of the numerical coefficient (0.01 m/s 0 5 ) accounts for a development of an internal
boundary layer on both sides of a flat leaf (Gates, 1980; see Appendix III).
In D78 the aerodynamic resistance between the bare ground and the canopy layer,
ras, is specified according to
s 1 CH[afu0+(l-af)ua]
(4.58)
where u0 is a characteristic wind speed within the canopy. The original parameterization for
u0 of D78 was replaced by taking «0 = u», as in the BATS-scheme. In the original D78 and BATS
schemes, the bulk drag coefficient CM was taken instead of CH, assumed equal for
momentum and heat.
The formulation of ras shows an inconsistency, due to the empirical nature of its
definition. A consequence of eq. 4.58 is that for oy < 1, ras depends on the choice of the
reference height zR via its dependence on ua, rather than solely on the aerodynamic transfer
within the canopy layer. Unreported comparisons between ras parameterized by D78 and by
Choudhury and Monteith (1988, see next section) show that both values approximate each
other in the EFEDA vineyard case for zR = 25 m, but that the D78 parameterization gives a
value approximately half as high as the Choudhury and Monteith value for 2 8 = 3 m (Van
den Hurk et al., 1995; section 5.2.2). Dickinson et al. (1986) chose a reference height of 1.3 m
above grass land. In a newer version of BATS (Dickinson et al., 1993), the dependence of ras
on zR was avoided by taking [0.004 u»]"1, where the numerical coefficient is a fixed value of
the transfer coefficient between the soil surface and the inside canopy air layer.
The leaf stomatal resistance in D78 depends on intercepted shortwave radiation and
soil moisture content only. In the current study, it was replaced by the parameterization
present in BATS and proposed by Noilhan and Planton (1989). rst depends also on vapour
pressure deficit and leaf temperature, and is given by a Jarvis-type model according to
4. Selected models 1 35
? l r . s,niin r r c
i"2i"3i"4
(4.59)
in which
1 _ w
r r s,min
/ +
r s,max
(4.60)
with ƒ = 0.55 K /LAI Kref, and K, a reference value,
h^-SD^c-%) ( 4-6 1 )
with gD a species-dependent coefficient,
F4 = 1 - 0.0016 (298 - Tcf <4-62>
and F2 given by eq. 4.28 with (0 = a>2.
4.1.5 The two-layer models of Shuttleworth & Wallace and Choudhury & Monteith • Model description
Shuttleworth and Wallace (1985, denoted as SW85) proposed a two-layer model
similar to D78, but based on a solution of the Penman-Monteith equation for both the canopy
and the underlying soil. The Penman-Monteith equation implicitly solves for the surface
temperature by linearizing dqsat/dT and combining the equations for H, XE and the total
amount of available energy. This strategy allows a direct computation of the surface fluxes,
without the need to define a surface temperature.
A resistance network sketched in Figure 4.10 is designed, and just like for D78 the
within-canopy temperature and vapour pressure are affected by the fluxes of each
component.
SW85 considered the partition of available energy, A (eq. 4.1), into sensible and latent
heat, by using the concept of surface resistance for both the canopy and the soil evaporation.
Unlike in D78, A is assumed known. The energy budgets for the canopy and soil are given as
Ac = Q.,c=Hc^Ec ( 4 - 6 3 )
and
A = Q - G = H+1EC (4.64)
The partitioning of net radiation over the canopy and the soil components is
parameterized by applying Beer's extinction using an extinction coefficient ßr:
Q , # s =Q.exp( -ß r LAJ) (4.65)
Implicitly it is assumed that the radiation absorbing material (the canopy leaves) are
• 136 Sparse canopy parameterizations for meteorological models
homogeneously distributed over the canopy layer, both horizontally and vertically. Dolman
(1993) adapted this simple partitioning by allowing for an exponential extinction in only a
part of the grid box, equivalent to defining a fraction of vegetation cover. Furthermore, he
allowed the presence of an understorey of vegetation, which was assumed to have the same
temperature as the underlying soil, for simplicity. These modifications were not included in
the current study.
Figure 4.10: Schematic layout of the models of Shuttleworth and Wallace (1985) and Choudhury and Monteith (1988). The components enclosed by the dashed box apply to the Choudhury and Monteith formalism only. For explanation of symbols: see text
Tc 'i
[ Canopy\ Î J - Ï '
Soil surface
z0m+d
j ~ ~ " -
ru
rl
A ?
•
Tl
T2
"~ i
z1 i
z2 !
SW85 elaborated the expressions for the canopy- and soil evaporation drawing up
separate PM-equations for each component, and eliminating the within-canopy water vapour
pressure deficit, D0. The total evaporation is given by
XE = Cc PMC + Cs PMS (4.66)
in which the coefficients PMS and PMC are given by
pcvD-ArcaAs
AA + .
PM„
a c r +r
A + y 1 + .
AA +
PM„ =
pcpD-AraAc
a s
A + y
(4.67)
rss is the soil resistance for evaporation, equivalent to rf. The coefficients Cc and Cs in eq.
4.66 are functions of the resistances in the network of Figure 4.10, written as
4. Selected models 137
1+ . RcK
W + Rf l )
-i R*R„ s a
RAK + K) (4.68)
where
Rc = (A + y ) rca + Y rc
s
(4.69)
The resistances are parameterized somewhat differently than in D78. The
aerodynamic resistance above the canopy, rf, includes a stability correction of the form
proposed by Choudhury et al. (1986):
K V -In
'zv-dV
'-Om
l+5g(zR-d)(T0-Ta)/(Tya) (4.70)
with x = 2 for stable and 0.75 for unstable conditions, respectively. The resistance to the soil,
ras, is obtained by integration of a (hypothetical) exponential profile of the eddy diffusivity
within a dense canopy (LAI > 4) between the surface and the level z0m + d, indicated by the
node in the resistance network. The final value of ras was found by a linear interpolation
between a full canopy cover and a bare soil. Alternatively, Choudhury and Monteith (1988,
denoted as CM88) parameterized ras by defining the effective source level, z0m + d dependent
on the canopy density and crop height, using the numerical simulations of Shaw and Pereira
(1982). Their final formulation of ras is written as
h exp(n)
nK(h) exp - exp
- " ( < * + z 0 m ) (4.71)
where z0 ' is the roughness length of the underlying soil, n an eddy-diffusivity extinction
coefficient, and K(h) the eddy-diffusivity at crop height h, given as K U» (h - d). The roughness
length and displacement height of a canopy with leaf area index LAI is fitted on the
simulations of Shaw and Pereira (1982) by the expressions
'0m 0.3 h
3hyß f \
i + ! h
\ J
0 < X < 0.2
0.2 < X < 1.5
(4.72a)
and
138 Sparse canopy parameterizations for meteorological models
1.1 h lul ( l + X 1 / 4 ) (4.72b)
with X given by Cd LAI, where Cd is the leaf drag coefficient. Shuttleworth and Gurney
(1990) showed that this formulation did not differ significantly from the parameterization of
sw85.
CM88 also use a vertical integration of the canopy wind profile to parameterize the
bulk boundary layer resistance, rac. Considering an exponential wind profile described by
use of an attenuation coefficient au (Cionco, 1972), the bulk boundary layer resistance is
given by
-1
r„ = LAI 0.02
V ) \
u(h)
L
r / vi
1 -exp _«« 2
v P.
(4.73)
No equivalent resistance is present in the pathway between the canopy air and the soil
surface. In the limit of a completely bare soil, the absence of an extra resistance for scalars
implies that momentum and scalars are exchanged at the same rate, and so z ^ = z0ft.
Unlike SW85, CM88 also specify the canopy resistance. It is assumed to be a function
of LAI and shortwave radiation only, according to
gctttLAI+glK\l-exp(-!irLAr)\ (4.74)
in which gj is a coefficient expressing the sensitivity of rsc to sunlight.
Apart from a different parameterization of some of the resistances in SW85, CM88
conceptually differs by including explicit expressions for the soil heat flux and soil
evaporation resistance. In their model, two soil layers are discerned: an unsaturated zone
close to the surface, and a saturated soil layer at a depth below the surface (see Figure 4.10).
Evaporation of soil water takes place at the intersection between the two soil layers. The
energy balance at the bare soil surface is therefore given by
^ * , s Hs + G0 (4.75)
where G0 is the soil heat transport downward from the surface. At the evaporation front the
energy balance equation reads
^ £ s - G o ~ G (4.76)
Both G0 and G are parameterized using a resistance formulation and a temperature gradient:
T _ T _f I (4.77) Go = PC
P-
and
4. Selected models 139
T1 ~T2 pc J l (4.78)
" r.
where pcp appears in eqs. 4.77 and 4.78 for numerical simplicity, and T1 is the temperature
at the layer interface, rather than the temperature of the upper slab. The upper and lower
exchange resistances are functions of the thermal properties of the soil and the
corresponding layer depth, according to
r = pc 2 l (4.79)
r, = pc„
' PM»J (4.80)
sat>
where Xj is treated as function of the soil moisture content (at saturation in the lowest soil
layer). The introduction of these resistances enabled CM88 to develop and additional PM-
equation for the soil evaporation, by writing
es«t(T i)- eo XES
Pc» (4.81) s s
and linearizing esat between T0 and Tv rf is a resistance for water vapour transport through
the upper (dry) soil layer, equivalent to SW85. An expression of rf, proposed by CM88,
includes a dependence on Dv and a tortuosity v.
rS = I fL (4.82)
Various (semi-)empirical expressions for rss exist (for instance, Camillo and Gurney,
1986; Dolman, 1993). Often this so-called ß-type evaporation scheme (Kondo et al, 1990) is
used in combination with a relative humidity in the soil pores, a , rather than assuming the
air in the pores to be saturated (Van de Griend and Owe, 1994). a is a function of the ma trie
potential \\f according to (Philip, 1957):
ap = exp^y /R^T) (4.83)
In CM88, a is assumed to be unity.
The depth of the upper soil layer, zv increases as soil evaporation proceeds. For a
constant value of <Dsa( in the saturated zone, the depth of the upper soil layer progresses
according to
140 Sparse canopy parameterizations for meteorological models
F . co , ^ f i (4.84) s sat d t
The entire set of equations describing the energy balance at both the soil and the
canopy surface is rather complicated and not repeated here.
A major physical drawback of the resistance parameterization of the soil heat flux is
that heat storage in the upper soil layer is ignored. A resistance equation as eq. 4.78 requires
that the heat flow is constant over the resistance pathway. In atmospheric heat transport this
requirement is roughly met, due to the low specific heat capacity of air. However, the
specific heat capacity of soil cannot be regarded to be negligible, and a constant flux is
hardly present, especially in soil layers close to the surface. A second point of criticism is the
assumption of a saturated zone near the surface. This situation may often occur in
agricultural farmland, where the soil water table is controlled to optimize crop production.
However, Mediterranean sparse canopies are usually characterized by a significant water
stress, and a saturated water table will seldom be found close to the surface in these areas.
These issues will be further adressed in section 5.3.
• Numerical stability of PM-type two-component models
Studies with coupled surface-PBL models carried out with surface models based on
the PM-equation consistently revealed problems with numerical stability. Three aspects
related to surface temperature are responsible for this problem: net radiation, stability
correction of rf and soil heat flux.
In a PM-type two component model both the canopy and bare soil temperature are
implicitly obtained by linearizing dqsat/dT. The models are diagnostic rather than
prognostic, and don't include time derivatives of for instance the canopy and bare soil
temperatures. Thus, with respect to the solution of the canopy and soil temperature, PM-
models are fully implicit, and therefore numerically very stable. However, when for instance
a dependence of net radiation on surface temperature is to be carried out, the equations
describing Q» and its partitioning should be incorporated in an implicit mode as well, in
order to gain advantage of the fully implicit character of the PM-model. Unfortunately, the
two layer models carry a large number of equations to solve for the surface temperatures
and fluxes, even with prescribed values of Q,, G and ra". Including implicit dependences of
these parameters on surface temperature is therefore a cumbersome job. Particularly under
stable conditions, when aerodynamic resistances are large, these surface temperatures are
very sensitive to the exact values of the sensible heat fluxes from the canopy layer to the
canopy and soil component. As these sensible heat fluxes are to a large extent determined by
net radiation, an unstable set of equations is readily obtained when an explicit formulation
is used for Q». Similar arguments are valid for including a stability correction in ra", or
describing soil heat flux, for instance by use of a force-restore method (as in the modified
big-leaf model, section 4.1.1).
Although Dolman (1993) claims his PM-type surface model to be designed for
application in GCM's, he tested it using measured values of Q» and G. Similar tests were
carried out by SW85 and CM88. However, to serve as surface description scheme in GCM's a
surface model should include a parameterization of these quantities. Dolman and Ashby
4. Selected models 1 41 •
(personal communication) are currently developing a numerical surface scheme in which the
multiple source surface model of Dolman (1993) is coupled to an implicit diffusion scheme
to describe heat and water fluxes in the soil. The implicit soil scheme describes a
temperature profile at time step n + 1 using adjacent temperatures in the same time step.
Dolman and Ashby are extending the numerical solution matrix for the soil temperatures
with two extra layers, situated at the canopy layer and the reference level above. The matrix
coefficients for the exchange between these two above-surface layers include the exchange
resistances for aerodynamic transport and available energy. The air temperatures are solved
at the implicit time step (n + 1), and can numerically be attached to the soil scheme. By the
time of finalizing this thesis a complete version of this algorithm was not yet available.
4.2 Treatment of the planetary boundary layer
In this study the development of the planetary boundary layer is described in
relation to the diffusion of heat, moisture and momentum in the lowest layers of the
atmosphere. Two turbulence regimes are considered: a fully convective regime during
daytime (the mixed layer), and a stable nocturnal PBL. Other stability regimes (Holtslag and
Nieuwstadt, 1986) are not considered in this study. For each regime profiles of the turbulent
diffusivity are constructed, based on appropriate scaling parameters.
The diffusion problem is solved by taking the surface fluxes as the lower boundary
condition. During daytime, entrainment processes at the top of the PBL are also incorporated.
The boundary layer depth, z(-, is explicitly evaluated from the simulated virtual temperature
profiles. The numerical diffusion scheme proposed by Troen and Mahrt (1986) is used to
solve the diffusion equations. The full model is described by Jacobs (1994), and below only a
brief summary is given. For the convective PBL a simple slab model is also used in chapter 6,
and this model is described briefly in section 4.2.2.
4.2.1 A numerical diffusion scheme for the planetary boundary layer
Fluxes of momentum and scalars in the PBL are parameterized using a simple local
first order closure scheme:
f \ K ds .. (4.85)
f as äz
V
\
-•h J
In this equation s denotes a constituent (s = m for momentum, h for heat and q for humidity),
Ks an eddy-diffusivity and ys a countergradient correction term, introduced by Deardorff
(1972). ys accounts for transport contributions from large turbulent structures, and its impact
is shown to be considerable for particularly highly convective conditions (Holtslag et ai,
1995).
For the daytime PBL, the eddy-diffusivities and countergradient corrections proposed
by Holtslag and Moeng (1991) are used. Ks is a function of the free convection velocity scale
if», the boundary layer height z(, and the entrainment ratio Rs, which represents the ratio of
the flux at the PBL-top to the surface flux of constituent s. w» is defined by
142 Sparse canopy parameterizations for meteorological models
w. = W 6 7 ,
ë v° V
1/3
(4.86)
Ys is a function of w», the surface heat flux and the profile of w1 , which was described
using an expression proposed by Lenschow et ah (1980).
Both Ks and ys were fitted on LES simulations carried out by Moeng and Wyngaard
(1984,1989). These simulations indicated that the pressure covariance term and the
turbulent transport term in the scalar flux equation differed by a constant value. This
indication was used to parameterize ys. Holtslag and Moeng (1991) suggested that the
parameterization of Ks and ys could be applied to both the heat and scalar flux equations.
However, strictly spoken the parameterization is valid in only a limited PBL-height range,
approximately between 0.1 and 0.8 z,. Jacobs (1994) argued that the difference between the
pressure covariance term and the turbulent transport term in the scalar flux equation may
well be constant in the centre of the PBL, but that this breaks down near the top, where the
entrainment of humidity is generally positive. This causes the pressure covariance term in
the scalar flux equation (- q Qv) to be positive rather than negative (Stull, 1988). He
therefore evaluated y at z/z(- = 0.4, and kept this countergradient term constant throughout
the entire PBL.
The LES simulations of Moeng and Wyngaard (1984) were carried out for two
classical situations: a positive scalar flux at the surface combined with a negative flux at the
top of the PBL (typical for temperature transport), and a positive scalar flux at both the
bottom and the top of the PBL (representative for humidity transport). A distinction between
bottom-up and top-down processes was carried out by simulating a situation with a
negative scalar flux at the PBL-top only. The difference between this transport and the typical
temperature transport enabled the definition of the bottom-up transport term for tempera
ture. A similar set-up for discerning between top-down and bottom-up processes for
moisture would consist of a LES simulation with a positive flux at the PBL-top only. This
simulation was not carried out by Moeng and Wyngaard (1984). An improvement of the
parameterization of y. could possibly be achieved by performing these additional LES
exercises (Michels and Holtslag, priv. communication). However, this aspect is beyond the
scope of this study, and we adopt the recommendations of Jacobs (1994) for further
calculations.
For the description of Ks in the nocturnal PBL we followed the original suggestions of
Troen and Mahrt (1986). Ks is expressed using a different velocity scale, ws, given by
Z (4.87)
in which §m is a stability function (Holtslag et ah, 1990). A smooth interpolation between
nocturnal and daytime diffusivity profiles is carried out by using w,/u, as indicator.
During each timestep the boundary layer height z, is diagnosed using a bulk-
4. Selected models 1 43
Richardson approach:
z _ * 'A|V(Z , ) | 2 (4.88) ' g(ep(z,-)-eg)
In this equation, Ric is a critical Richardson number, which is a measure for the largest
stability where turbulence can still exist. Ric is taken to be 0.25. Furthermore, V is the
horizontal wind speed, and 9S a measure of the temperature excess of the thermals,
parameterized using the surface buoyancy flux and the temperature at the z - zR. In all cases
a minimum value of 0.175 K «»/ƒ is taken for z;-, which is a suggested value of the near-
neutral PBL-height scale, including the effects of geostrophic wind shear (Koracin and
Berkowicz, 1988). ƒ is the Coriolis parameter, equal to 2i2sin4>.
The entrainment ratio Rs is evaluated from the calculated flux profile in past time
steps. Rh is defined as the ratio of the minimum heat flux to the surface flux. Generally, the
level where the heat flux is minimum (zmin) is found slightly below z •. As pointed out by
Jacobs (1994), the entrainment ratio for humidity is prone to numerical fluctuations when
evaluated at the same level as Rh. Therefore, Rq was specified as w q (z =0.8 zmin) / w q 0.
Both Rh and Rq are set to zero for stable conditions. In order to increase numerical stability
new values for Rh and R are evaluated only every ten minutes of simulation.
During every time step the wind profile is adjusted by a geostrophic forcing,
determined by the geostrophic wind speed V . Numerical experiments have shown that this
geostrophic forcing can yield strong oscillations of the wind field with a frequency ~f and
amplitude ~V . For these reasons the geostrophic acceleration was only applied at levels
within the PBL. Also, the wind, temperature and humidity profiles above the PBL were
unchanged in the simulations.
4.2.2 Slab-model for the convective PBL Tennekes (1973) and Driedonks (1981,1982a) discuss the treatment of the convective
boundary layer by use of a so-called slab model. The model treats the boundary layer as a
box heated from both below and above. Air within that box is instantaneously mixed, and
its average temperature 6m is a function of the net heat supplied both from below and from
above, and of the height of the box. Driedonks (1981) derived analytical expressions for the
sensitivity of z- and 0m to the total amount of sensible heat released by the surface, and to
the initial profile of 9. A simple heat entrainment closure was adopted. McNaughton and
Spriggs (1986) applied the approach of Driedonks to describe evaporation into a convective
boundary layer.
The slab model elaborated by Driedonks (1981) describes the growth of the PBL as
dz,- w Qve (4.89)
df Afi,
where AQV is the inversion strength at the top of the boundary layer, and w %v is an
entrainment buoyancy flux at the top of the PBL.
• 144 Sparse canopy parameterizations for meteorological models
A simple closure of w'dv is not easy to give, since sensible and latent heat transport
both contribute to this term. However, for a dry convective boundary layer, w/Qv ~ urfr .
A simple closure consists of relating w 9 e to the surface heat flux, w 9 0 , according to
w®e = Rh^0 <4-9°>
Tennekes (1973) also considered the contribution of mechanical turbulence to the
entrainment flux, but this is ignored here. By definition of the integrated surface heat flux as
t
KOsJVeV^dt' W-W o
Driedonks (1981) expressed the development of zi as
z2 ( l+2R„)(j-50e) ( 4 9 2 )
0.5 Ye
where 80e is the initial heat content, given by zl0A90 - 0.5yezl0
2, and y e is the temperature
slope above the PBL. This expression predicts that for a constant value of y e and Rh the PBL 1 l'y
height increases as function oil .
Similarly, the value of the mixed layer temperature, 9m, can be expressed as function
of z-, for a given value of y e and Rh:
e m ( 0 = e 0 0 + Y e ^ ~ - z , . ( t ) W.93)
where 900 is the value of 9 when Ye is extrapolated to z = 0. The rate equation for the
temperature jump A9 is given by
A9=Y f l — z , (4-94) 9 1 + 2 R , '
The dependence of the specific humidity of the PBL on the total integrated surface
latent heat flux ƒ, defined as
t
7?.(AM' (4-95) J(t) = j H ^ f / j d t '
is a more complex function. The rate of change of the mixed layer specific humidity, qm, is
written as (Driedonks, 1981; McNaughton and Spriggs, 1986)
4. Selected models 1 45
dt
(4.96)
The second term between brackets in eq. 4.96 indicates the transport of moisture at
the top of the PBL. A rfetrainment is simulated if the specific humidity jump Aq is negative.
The entrainment rate dz(/df is given by eq. 4.89, while Aq is equal to
^ M O O + z i V ? m ( 4-9 7 )
where q00 and y have the same meaning as 600 and y e . Aq also changes as time proceeds,
and an analytical expression for dqm/dt is not easy to give. In chapter 6, eq. 4.96 will be
solved numerically by taking Aq, calculated from eq. 4.97, from the previous time step.
4.3 Limitations to the coupled 1-dimensional atmospheric model
The study reported in this thesis is designed to evaluate the sensitivity of the
predicted PBL-development to the parameterization of the underlying (sparsely vegetated)
surface. Later in this study computer simulations will be compared to field measurements
(chapters 5 and 6). However, the conclusions to be drawn are confined to the processes that
are included in the simulations. It is therefore of interest to pay some attention to the
physical processes which were not included in the models described above. These may play
a role in the complex surface-atmosphere interaction which is the subject of this study.
First of all, the coupled SL-PBL model is essentially one-dimensional. Computations
are carried out and compared to data under the assumption that the forcings apply to a
homogeneous fetch of unlimited horizontal dimension. In practice, advection of warm dry
air has modified the measured profiles considerably for many days (see section 6.5.1). The
radiosoundings also revealed the existence of a clear and persistent sea wind as far as the
Tomelloso area (Bessemoulin, priv. communication).
A second limitation of the model is that processes associated with clouds are not
included. Especially the radiative properties may be of importance for the net radiation at
the surface or the temperature profiles in higher air layers.
Third, longwave radiative cooling was not regarded. This process in practice results
in a decrease of the temperature of the air near the surface of 1 - 2 K per 24 hrs (Garratt,
1992). Stronger cooling takes place near the surface than at higher altitude, which causes the
development of a slightly stable stratification in the residual layer during nighttime, when
vertical mixing is absent. This stable lapse rate limits the growth speed of the convective PBL,
and ignoring this process may lead to an overestimation of this growth speed. However, the
exact rate of the cooling in each layer depends on the distribution of greenhouse gases in the
air masses above and below the particular layer, of which water vapour and C 0 2 are present
in the highest concentrations.
Also, large scale processes like subsidence were not included. This process is caused
by descending air motions in the centre of high pressure areas, and reduces the boundary
layer height.
• 146 Sparse canopy parameterizations for meteorological models
The entrainment equations in both the numerical and the slab model regard buoyant turbulence only. Turbulence induced by for instance wind shear near the top of the PBL is
not included.
Furthermore, sensitivity analyses in chapters 5 and 6 were confined to simulation
periods of five days at most. This is a rather short time scale for considering
parameterization effects on for instance soil moisture content. Shao et al. (1994) compared
various soil moisture parameterizations of land surface schemes, and suggest that datasets
of at least one year are required for an adequate model evaluation.
Finally, the one-dimensional origin of the model simulations does not allow to
include pressure effects on wind flow or the influence of baroclinicity (thermal winds). For instance, the Coriolis force can result in a very strong oscillation of the wind speed
within the PBL (see above). In the real world, these oscillations will probably be damped due
to the building up of high pressure areas, which will change the geostrophic wind direction.
This damping effect was not accounted for, and the simulated wind profiles appeared to be
rather unrealistic in some occasions. However, note that one-dimensional simulations are
essentially inadequate for investigations of the wind profile and its changes in time, since
the horizontal morion of air is a two-dimensional problem. We therefore pay only little
attention to simulated wind profiles.
4. Selected models 1 47
5 If you think about a problem during the night, and think
about it again the next morning, you get different answers
An intercomparison of three soil/vegetation models for a sparse vineyard canopy1
For GCM's the lower boundary condition is often provided by a Soil-Vegetation-
Atmosphere-Transfer (SVAT) model. As pointed out in the introduction section of this study,
the description of the exchange processes between the surface and the atmosphere is of great
influence on the long term predictions of these larger scale models.
Obviously, a SVAT intended to provide the lower boundary condition in GCM's needs
to be able to describe a wide range of surface types, varying from completely vegetated to
sparsely vegetated or completely bare surfaces. Sparse canopy surfaces exhibit rather
demanding features with respect to the exchange of momentum, scalars and heat between
the surface and the atmosphere. Here, we focus on three aspects: aerodynamic exchange,
soil heat flux and surface evaporation.
For the aerodynamic exchange, a difference is made between the exchange of
momentum and of scalars as heat, water vapour, C0 2 or trace gases. Surface roughness
elements acting as a momentum sink are usually parameterized by extrapolation of the
wind profile to a hypothetical sink level at height d + z0m. Both parameters depend on the
presence of roughness elements, characterized by the surface fraction being covered, and the
spacing and height of the elements. Measurements and theoretical considerations reveal a
difference between the exchange rates of scalars and momentum. The transport of water
vapour, heat or trace gasses is considered less efficient than momentum transport in most
cases, owing to the absence of bluff-body forces for scalar exchange (Thorn, 1972; Beljaars
and Holtslag, 1991). Models treating the surface as a single homogeneous layer impose an
'excess' resistance for scalars to account for this effect, equivalent to adopting a different
roughness length for scalars, zoh (section 2.4.2). Experimental quantification of this
roughness length has been carried out for many surface types, particularly using radiometric
1 Adapted from Van den Hurk et ai (1995)
148 Sparse canopy parameterizations for meteorological models
surface temperature measurements (Garratt, 1978; Huband and Monteith, 1986; Kustas et ah,
1989).
For sparse canopies the interpretation of z0h is far from straightforward. The heat
exchange takes place at various levels, and the source distribution is determined by various
environmental parameters, such as radiation, canopy evaporation, or forced convection.
Two-layer models avoid the definition of a single source level by parameterizing the
sensible and latent heat exchange at two separate levels: the canopy and the underlying
substrate. The absence of bluff-body forces for scalar exchange is accounted for by
additional resistances within the canopy layer. The turbulent exchange of sensible and latent
heat between the canopy, the substrate and the air above are treated separately.
Parameterization of these resistances is carried out by adopting assumptions about the
turbulent exchange within the canopy layer and the effective sink level. This level can either
be a fixed function of the canopy height (Shuttleworth and Wallace, 1985), a more complex
function of leaf area index (Choudhury and Monteith, 1988), or crop density (Raupach,
1992). However, turbulence characteristics within the canopy layer are rather complex and
not easily defined using simple parameters (McNaughton and Van den Hurk, 1995).
Blyth and Dolman (1995) used a two-layer model to explore the value of z0m/z0il for
a sparse canopy. The apparent aerodynamic resistance for heat transfer, ra, was deduced
from the simulated total sensible heat flux density H, the air temperature Tfl, and a mean
surface temperature T sur, according to (see also eq. 2.35)
T sur " Ta (5.1) r - pc v
T sur was obtained from a linear interpolation of the model predictions of canopy
temperature Tc and ground temperature T$:
Tsur = ofTc + (l-cf)Ts (5-2)
The value of zoh is then obtained from eq. 2.36. The resulting roughness length for heat
appeared to be no function of the surface itself (as is the case for z0m), but it showed a clear
variation with radiation, wind and even vapour pressure deficit. Apparently, the variation
of the distribution of the heat sources causes the variation of zoh. Similar results were
obtained experimentally by Kustas et al. (1989), Verhoef (1995), and in section 2.4.2.
The second issue of interest for sparse canopy surfaces is the treatment of the soil
heat flux density. Under conditions where a significant part of the radiant energy reaches
the bare soil, a relatively large part of this energy is associated with heating and cooling of
the upper soil layers. An accurate description of long term thermal dynamics of such a
sparse canopy surface requires a proper description of the heat transfer into the soil. Since
for strongly irradiated, dry soils large temperature gradients can be present near the surface,
the description of the soil heat flux is likely to depend on the selected number and thickness
of the soil layers, and the parameterization of the thermal conductivity of the soil.
The third issue involves evaporation from a sparse canopy surface and dewfall onto
it. The water vapour transport from a sparse canopy surface into the atmosphere is a
5. An intercomparison of 3 SVAT's 149 •
mixture of transpiration from the canopy elements and evaporation from the bare soil
component or from intercepted water. During the process of dew formation, water vapour is
transported downward from the atmosphere (dewfall), or it condensates immediately after
being released by the underlying soil (dewrise).
This section is dedicated to a comparison of various SVAT schemes using a common
dataset collected over a sparse vineyard canopy surface for five consecutive days, with
particular attention to the issues addressed above. The SVAT schemes include a one layer
model currently in use in the ECMWF global weather prediction model (Viterbo and Beljaars,
1995, VB95) and two dual-source models, published by Choudhury and Monteith (1988,
CM88) and Deardorff (1978, D78). In each of these models the algorithms to describe soil heat
flux density and aerodynamic transfer are based on different physical concepts (see chapter
4 for a description of these models).
The intercomparison serves two purposes. First, a qualitative and quantitative
evaluation of these different process treatments is of interest as these algorithms are often
applied in large scale atmospheric models. Second, the results will be used to construct a
reference SVAT, to be used in the coupled PBL-SVAT simulations in the next chapter.
Both in nature and in the model simulations the governing parameters show many
complex feedbacks, and individual processes can not easily be investigated in an isolated
way. Model errors related to one process of the transfer between surface and atmosphere
can cause significant discrepancies for the description of other processes. Despite this
feature, the comparison between the models and the observations will be separated into
three process categories: soil heat flux density, aerodynamic exchange of heat, and
evaporation and soil water balance.
L Description of data, model settings and used forcings
5.1.1 Collected data Data were collected during the regional scale EFEDA experiment (Bolle et al., 1993) in
a dry, semi-arid sparsely vegetated vineyard near Tomelloso, La Mancha, Spain. A detailed
description of the site and vegetation is given in section 2.2.
Measurements consisted of both forcings and flux densities to validate model results.
Atmospheric forcings were measured at a reference level of 2.95 m height, and consisted of
air temperature, air humidity, horizontal wind speed, incoming and reflected shortwave
radiation and net radiation. Longwave downward radiation L was parameterized by
closing the surface radiation balance, eq. 2.1. In this equation, the values of global radiation
(K ) and net radiation (Q.) were measured, the albedo (a) and longwave emissivity (es) were
taken as in the simulations (see below), and an effective surface temperature ( T sur) was
taken from measurements using an infrared sensor mounted at 3 m above the soil surface on
a cable and moved along a transect of 35 m. The transect included both canopy elements
and bare soil. Individual canopy and bare soil temperatures were extracted from the record
of temperatures. Soil temperatures were measured at five levels between 0.03 and 0.50 m
depth. Energy fluxes were selected from the available data as outlined in section 2.4.3.
Corrections to these fluxes are discussed in Appendix II.
Aerodynamic roughness z0m and zero plane displacement d were determined from
• 150 Sparse canopy parameterizations for meteorological models
wind profile measurements at four levels between 1.5 and 10.0 m. These quantities changed
considerably due to the vegetation growth (see section 2.4.1).
Soil moisture measurements were carried out at a few days before and during the
comparison period by the Dept. of Water Resources of the Wageningen University, using
TDR at 0.10 m intervals to 0.50 m depth (Droogers et al., 1993). Leaf resistance to water
vapour transport was measured from sunrise until sunset once every two days by use of a
dynamic diffusion porometer. After extensive quality control on data and calibration
(Jacobs, 1994), a crop resistance was obtained by averaging the measurements using a
weighing based on leaf age and light exposure (section 2.2.7). Measurements of leaf area
index, LAI, and fraction of vegetation cover, oy, were taken as described before.
5.1.2 Forcings and specific model settings
The simulations were carried out using observations taken between 19 June (DOY
170) 20:00 GMT, and 24 June (DOY 175) 24:00 GMT. For each model the simulation time step
was 600 s, and observations averaged to half hour intervals were interpolated to match the
time discretization.
All three models use measured values of temperature, wind speed and humidity at a
reference height above the canopy, and initial soil temperature and soil moisture profiles.
Observations of total net radiation were used as input for CM88, and shortwave and
longwave incoming radiation for VB95 and D78. However, during the nocturnal periods
following DOY 173 and 174 some data are missing due to failure of the measurement system.
Linear interpolation was used to estimate missing data. Initial soil moisture and temperature
profiles can be found in Table 5.1, for each of the models. Temperatures and moisture
contents in soil layers deeper than measured were assumed to be identical to the values at
0.50 m depth at the starting time of the simulation. Figure 5.1 displays the atmospheric
forcings.
To make the comparison of the models as straightforward as possible, most model
settings were adjusted to give similar surface and vegetation specifications. However, since
all models treat several parameters differently, some choices had to be made. A summary of
all model settings can be found in Table 5.2.
• VB95
In the original paper of VB95 universal functions describing the physical properties of
the soil are used for each soil type. However, we adjusted these parameters according to the
suggestions made by Noilhan and Planton (1989) for a sandy loam soil type (see Table 5.2).
The surface albedo was fixed at the measured value 0.29 for both the vegetation and soil
components, and for the longwave emissivity a value of 0.98 was taken (Bolle and
Streckenbach, 1993). In the operational ECMWF version of VB95, the aerodynamic roughness
length is a specified quantity for each grid box. Here, calculated aerodynamic roughness and
zero plane displacement were taken. The value of z ^ increased from 0.035 m at DOY 171 to
0.043 m at DOY 175, whereas d was kept constant at 0.35 m in this limited time range. Note
that these values are relatively small, regarding the observed canopy height exceeding 0.80
m at all times (Wieringa, 1993). A different aerodynamic roughness for heat was calculated,
using zOm/z0h = 200. Note that this value is an order of magnitude larger than the value
5. An intercomparison of 3 SVAT's 151 •
suggested by Braud et al. (1993), who simulated the energy balance of a similar sparsely
vegetated vineyard using the scheme of Noilhan and Planton (1989). Since the sensible heat
flux is the dominant term of the surface energy budget for a dry sparse canopy surface, the
choice for z0m/zoh will reflect the difference between the mean level of the momentum sink
(the canopy elements) and the heat source (the underlying bare soil). The apparent
conductivity of the skin layer was kept at the suggested value of 7 W/m2K. Since exact
information about the root distribution was not available, the rooting depth of the
vegetation was defined according to the original suggestion (1 m, with water extracted
equally from the top three layers). The response of the canopy resistance to light and soil
moisture was parameterized according to VB95. In the simulation period LAI increased from
0.29 m 2 /m 2 on DOY 171 to 0.35 m 2 /m 2 on DOY 175, whereas oy increased from 0.10 to 0.12 in
the same period.
Table 5.1: Initial values of soil moisture and soil temperature for each model
Parameter Depth (m) D78 CM88 VB95
SoU temperature (K) 0 293.09 293.09 293.09
0.07 302.96
0.10 303.21
0.28 298.66
0.50 296.09 296.09
1.00 296.09
2.89 296.09
Soil moisture content (m3 /m3) 0.07 0.07
0.10 0.07
0.28 0.08
0.50 0.15
1.00 0.15
2JÎ9 015
• CM88
CM88 uses principally net radiation, wind speed, humidity and air temperature as
forcing functions. For this comparison, the deep soil temperature was taken from
measurements at 0.50 m depth, rather than taking it as constant. The absence of a saturated
zone near the surface made a formal justification for choosing the value of the depth of the
top soil layer, z2 impossible. Zj was taken to be 0.40 m, to get a high soil evaporation
resistance corresponding to a small soil evaporation expected from a dry soil surface. For the
thermal conductivity in the top layer a value of 0.3 W/mK was adopted, and in the bottom
layer 0.5 W/mK, following Verhoef et al. (1995). Directly measured values of LAI and crop
height, h, were adopted. Roughness length and displacement were computed as function of
LAI and h, assuming a leaf drag coefficient of 0.2 (Choudhury and Monteith, 1988).
Characteristic leaf size, necessary for computing the crop boundary resistance rflc, was
0.05 m. Since explicit calibration coefficients of the response function for stomata to radiation
• 152 Sparse canopy paramelerimtions for meteorological models
are not given by CM88, the function was calibrated using porometry measurements taken at
several days in the measurement period (see Table 5.2).
Figure 5.1: Meteorological forcings of the simulations: (upper left panel:) air temperature ( ) and absolute humidity (•—•); (upper right panel:) horizontal wind speed, and (low panel:) incoming shortwave ( ), incoming longwave ( ) and net (•••••) radiation
• D78
For D78, z0m and d were computed using the same formulation as CM88. The
thickness of the top soil layer was fixed at 0.1 m, and the deep soil temperature varied with
a seasonal cycle as suggested in the original paper. The crop resistance was parameterized
as function of radiation, air temperature, atmospheric humidity and soil moisture, following
the general suggestions made by Noilhan and Planton (1989).
Similar soil physical quantities were taken as for VB95, that is, the sandy loam soil
type (see Table 5.2). The surface albedo was fixed at the observed value (0.29), and the
surface longwave emissivity was taken the same as in VB95 (0.98 for both plants and soil).
5.2 Simulations with the SVAT-schemes
The sparse canopy surface for which the simulation was carried out has some
pronounced properties with respect to the partition of energy over the various components.
First, unlike in case of densely vegetated surfaces, the soil heat flux density is an important
component of the surface energy balance for the current data set. Due to the small relative
area covered by the plants (maximum 12%), approximately 30% of the total daytime net
5. An intercomparison of 3 SVAT'S 153
radiation was used to heat the soil. The daily averaged soil heat flux density was
approximately 20 W/m 2 , indicating a temperature increase in deeper soil layers at this time
of the year.
Second, the surface net radiation is hardly used for evaporation (< 10% of net
radiation, generally), but a clear distinction between the canopy and the underlying soil is
present in terms of latent and sensible heat exchange and surface temperature. Sensible heat
(about 60% of net radiation) was released mainly by the warm substrate, whereas the
evaporation, which was dominated by the canopy, caused the vegetation to be significantly
cooler than the surrounding bare soil.
Third, the large rooting depth enabled the vegetation to transpire in spite of a very
dry top soil. Stomatal responses to the moisture content in the top soil layer are expected to
be small.
The models faced the challenge of simulating these features. The simulations will be
compared with attention focused on three aspects: soil heat flux density, sensible heat
transfer between the surface and the atmosphere, and evaporation in combination with soil
moisture budget.
Table 5.2: Model parameter values
Parameter
General configuration time step (s)
depth of soil layers (m)
Vegetation dimensions crop height (m)
Leaf Area Index
fraction vegetation cover
characteristic leaf size
Aerodynamics roughness length (m)
displacement height (m)
soil roughness length (m)
roughness length for heat (m)
leaf drag coefficient
reference height (m)
non-evaporating parts factor
extinction coefficient for wind speed
extinction coefficient for eddy diffusivity
symbol
f
zi z2 z3 z4
h
LAI
af
L
z0m
à
zo' z0h
cd ZR
n au
n
eq(s).
_
4.71 - 4.72
multiple
multiple
4.57,4.73
4.5,4.70, 4.71
4.5, 4.70, 4.71
4.71
4.6
4.72
4.5, 4.70
4.40,4.56
4.73
4.71
D78
600
0.10 0.50
1
0.29-
0.10-
0.05
((LAI
0.35
0.12
h,Cd)
({LAI, h, Cd)
0.01
-0.2
2.95
1.1
-
-
CM88
600
0.40 (start) 0.50
1
0.29 - 0.35
0.10-0.12
0.05
i(LAl,h,Cd)
i(LAI,h,Cd)
0.01
-0.2
2.95
-3
2.5
VB95
600
0.07 0.28 1.00 2.89
-
0.29 - 0.35
0.10 - 0.12
-
0.035 - 0.043
0.35
-W200
-2.95
--
-
154 Sparse canopy parameterizations for meteorological models
Parameter symbol eq(s). D78 CM88 VB95
Radiation soil albedo
canopy albedo
surface emissivity
extinction coefficient for net radiation
Canopy resistance minimum crop resistance (s/m)
maximum crop resistance
cuticular conductance (m/s)
change of conductance per unit shortwave radiation (m/s / W/m 2 )
as
ac
Es
ß,
r s,nun
rs,max
Scut
Si
4.15, 4.36
4.15,4.36
4.15, 4.37 - 4.39
4.65,4.74
4.26, 4.59
4.60
4.74
4.74
0.29
0.29
0.98
-
125
5000
--
coefficients for PAR-response
coefficient for force-restore humidity transport
4.27
reference shortwave radiation (W/m2)
humidity response coefficient (Pa"1)
maximum dew reservoir depth (mm)
Soil parameters skin conductivity (W/m2K)
averaging coefficient for soil surface relative humidity
thermal conductivity top soil layer (W/mK)
thermal conductivity other soil layers, i (W/mK)
Retention curve coefficient
saturated soil moisture (m 3 /m )
field capacity (m3 /m3)
wilting point (m3 /m3)
tortuosity
saturated hydraulic pressure (m)
saturated hydraulic conductivity (m/s)
coefficients for o)
Kref
So
wmax
A
'c
XT1
A.T,
b
«>sat
% «w T
Vsal
Y»t
requ
4.60
4.61
4.20, 4.23, 4.44,4.46
4.14
4.19
4.9, 4.48, 4.79
4.9, 4.49, 4.80
4.10,4.12, 4.13
4.10, 4.12, 4.13, 4.51, 4.53, 4.84
4.19, 4.28
4.28
4.52,4.82
4.10,4.13
4.12
4.53
100
0.00025
0.8
-
1
f(0),)
f((0,)
4.90
0.472
0.354
0.075
0.66
-0.25
3.41 10"5
0.219 4
-Irej 4.51 1.8
0.7
0.0005
4 10"*
0.3
0.5
0.472
0.29
0.29
0.98
240
0.19 1128 30.8
0.8 ((LAI, oy)
7
1.6
f(COj)
f(CÛ;)
4.90
0.472
0.354
0.075
-0.25
3.41 10"5
5. An intercomparison of 3 SVAT's 155 •
5.2.1 Soil heat flux density
Figure 5.2 gives the measured and simulated soil heat flux density for DOY 171 -175.
As can be seen, the differences between the model predictions are very large. D78, using a
force-restore method to compute the soil heat flux density, gives a very good agreement
with observations. A small underestimation is present early in the comparison period. The
relatively slow response of the deep soil temperature to surface forcings results in a clear
phase shift of the soil heat flux density compared to net radiation (detailed in Figure 5.3),
which is well simulated by D78.
Also VB95 simulates a maximum soil heat flux density somewhat before local noon,
albeit less pronounced than D78. The soil heat flux density is on average about 30% too small
compared to the observations. This underestimation is not caused by a discrepancy between
the observed substrate temperature and the simulated skin layer temperature (Figure 5.7).
Obviously, the chosen value of the skin conductivity, A, plays a significant role in this
aspect.
173 174 date
176
Figure 5.2: Soil heat flux density for all comparison days. * observations; D78; VB95; CM88
The soil heat flux density predicted by CM88 is much too small compared to the
observations, in spite of using measured values of the thermal conductivity in the two soil
layers (see Table 5.2). The underestimation is almost a factor 10, and is too large to be related
to the choice of the initial dry soil layer depth (zj). Taking z2 0.01 m rather than 0.40 m at the
first time step increases the soil heat flux only by a few percent (figures not shown). Also, a
phase shift with respect to the local noon is not simulated by CM88 (see Figure 5.3). Only by
increasing the thermal conductivity to unlikely high values (exceeding 5 W/mK for the top
soil layer) can the maximum of the simulated soil heat flux be matched to the maximum of
the observed values, but not at the right time with respect to the local noon. The reason for
the discrepancy between model and data is the absence of a heat capacity in the upper soil
layer. The use of a resistance to regulate the heat flux in CM88 implies that no heat loss
occurs in this layer. Hence, the soil heat flux will always respond immediately to the forcing
156 Sparse canopy parameterizations for meteorological models
at the surface, and a phase shift will not be present in the calculations.
As a result of the underestimation of the predicted soil heat flux density by CM88, a
large part of the net radiation is available for XE and H, and causes a clear overestimation of
these two terms. This overestimation is reflected in the plot of the simulated substrate
temperature, shown in Figure 5.4, which is high compared to the radiometric observations
of the bare soil temperature.
Figure 5.3: Measured and simulated soil heat flux density for DOY 171; » observations; D78; VB95;
CM88
350
176
Figure 5.4: Measured (») and simulated (••••-) bare soil temperature. Only simulations by CM88 with computed soil heat flux densities are shown
date
The overestimation of the prediction of H and XE makes a comparison of the
parameterization of e.g. the aerodynamic exchange by CM88 with other models impossible.
With respect to this aerodynamic exchange a fair comparison between CM88 and D78 is
particularly useful, since these models use different formulations for aerodynamic
resistances in a similar resistance network (Figures 4.9 and 4.10). Therefore, in the following
the computed soil heat flux computation in CM88 is replaced by values of G as computed by
D78 which are very close to the observations (Figure 5.2). A comparison of H and A.E from
CM88 and VB95 is somewhat biased by the difference of G computed by D78 and VB95, and
5. An intercomparison of 3 SILT'S 157
must be carried out with caution. The soil evaporation in CM88 is treated as before, using a
resistance for water vapour transfer at the soil surface interface which increases as soil
evaporation progresses. A model of this form is essentially comparable to the model
presented by Shuttleworth and Gurney (1990), who adapted the original two-layer model of
Shuttleworth and Wallace (1985) with the parameterization of the aerodynamic parameters
according to CM88.
5.2.2 Sensible heat exchange and surface temperature
For the surface considered the aerodynamic exchange of heat between the surface
and the reference level is dominated by the contribution of the bare soil component. This
exchange can be separated in two segments for each model: a transfer above the canopy
equivalent to momentum transfer, and an extra resistance to account for the difference
between heat and momentum transport. In VB95 this difference is accounted for by taking z0m/z0h > 1' w hi l e in CM88 and D78 this extra resistance consists of ra
c and ras (see Figures 4.9
and 4.10).
Figure 5.5: Aerodynamic resistance within canopy for D78 and CM88, and excess resistance for VB95, as function of measured wind speed at reference level. Only simulation points are shown for which H > 0; • D78; O VB95; * CM88
Ujfm/s)
The aerodynamic resistance above the canopy, raa, is a function of the reference wind
speed, the roughness length z0m and a stability correction. The estimation of z0m from LAI
and h as applied in CM88 and D78 resulted in a value of 0.082 cm at DOY 171, slowly
increasing to 0.095 cm at DOY 175, exceeding the observed roughness length by a factor two.
The measured friction velocity, u», was overestimated by CM88 and D78, and reproduced
very well by VB95 (figure not shown). The latter was to be expected from the adoption of
measured values of z0m. The slightly different stability corrections in CM88 and D78 hardly
resulted in different values of u, and rflfl.
Figure 5.5 shows the values of the aerodynamic resistance between the soil and the
canopy layer (ras, for D78 and CM88) and the excess resistance applicable for z0m/zoft = 200
for VB95, for unstable conditions. A clear difference between CM88 and D78 is present in the
values adopted for ras, CM88 giving a value roughly twice as high as D78. The CM88
parameterization corresponds closely to the excess resistance adopted by VB95 for daytime
158 Sparse canopy parameterizations for meteorological models
situations. The implications of the parameterization of ras and the excess resistance are
demonstrated well by the relationship between the bare soil temperature and the total
sensible heat flux density, since the sensible heat released by the canopy is only a small part
of the total sensible heat exchange. CM88 and VB95 succeed very well in predicting both the
total sensible heat flux density (Figure 5.6) and the bare soil temperature (Figure 5.7). D78
underestimates the bare soil temperature by at most 7 K around noon, and overestimates the
sensible heat flux density by up to 100 W/m 2 . A small part of this overestimation is
associated with an enhanced net radiation due to lower surface temperatures.
500
Figure 5.6: Measured and simulated total sensible heat flux density; » observations; D78;
VB95; CM88
173 174 date
176
The performance of VB95 is very good for both sensible heat flux and surface
temperature, since values of z0m and zQh were obtained from field measurements. A small
overestimation of the sensible heat flux density is present for the first simulation day.
Obviously, the choice for the value of z0m/z0?J is an important parameter for a proper
description of the sensible heat transfer between the surface and the atmosphere. An
evaluation of z0m/zoh using measured soil and canopy temperatures reveals a clear variation
as time proceeds, both diurnally and for the five consecutive days (Figure 2.13). A similar
figure appeared by using the model of CM88 as outlined in eqs. 5.1 - 5.2 and 2.36. A clear
increase during the day can be seen, which can be interpreted as a reduction of the effective
level of the sensible heat source as the bare ground gets warmer. Taking z0m /zoh = 200 for
the whole period appears a good estimate for all days except the first.
5. An intercomparison of 3 SVAT's 159
330-
320-
9>
pera
tu
o
| 300
ä 290'
280
97n-
4 , 1/ U ü ï 1 fl
f I; f L %s, r
• > J A ^ f c ï i
£3FL ÄP
» 7 & r
*V f
l A 1 f \ 1 if v
W Ir i^ Y\ 1 Vv \ f V»
'*
à ff 1 'T M f \
ir ®j
f
Figure 5.7: Measured and simulated bare soil temperature for CM88 and D78, and skin temperature for VB95; * observations; D78;
VB95; CM88
171 172 173 174 175 176 date
5.2.3 Evaporation and soil water budget
VB95 and D78 underestimate the total evaporation during the entire comparison
period, while CM88 gives a small but consistent overestimation (Figure 5.8). The evaporated
water originates almost entirely from the canopy in CM88, since soil evaporation is limited to
low values by selecting a large top soil layer depth (Figure 5.9). Unlike CM88 and VB95, D78
computes a significant soil evaporation in the early hours after sunrise. The strong diurnal
variation of the moisture content in the top soil layer, C0j (Figure 5.10) causes the humidity at
the soil surface to reach values which are higher than the humidity in the canopy layer,
giving rise to pronounced soil evaporation. Once the top soil layer has lost enough water to
for the relative humidity at the soil surface to drop below the canopy specific humidity, q0,
soil evaporation suddenly ends.
Due to the different vertical resolution of the numerical schemes used to describe the
soil moisture content adopted by VB95 and D78, the dynamics of the top soil moisture
content, (0j, differs significantly for both models. In D78 C0j is much lower than the moisture
content in the bulk soil layer, while this difference is small in VB95 (Figure 5.10). As a result,
diurnal variations of C0j are strongly damped in VB95. The calculated soil moisture content in
the root zone decreases much stronger in VB95 than in D78, in spite of a similar canopy
evaporation rate (see below). The stronger decrease in VB95 is a direct result of the
simulation of water drainage to lower soil layers, not accounted for in D78. For longer term
predictions these different approaches can lead to significant differences in predicted soil
moisture content in the root zone. Unfortunately, the measurements of co were taken only
once during the comparison period, and these values were used to initialize the model runs.
Therefore, a detailed comparison between model runs and observations is not possible.
The canopy evaporation rate is predicted rather differently by the various models.
Since the crop resistance is usually approximately an order of magnitude larger than the
other resistances in the pathway between the canopy and the reference level, the
parameterization of rsc is of critical importance for the prediction of the canopy evaporation.
Figure 5.11 shows values of computed crop resistances, combined with porometry data.
160 Sparse canopy parameterizations for meteorological models
Also shown are values of rsc obtained from measured evaporation rates and leaf
temperatures, by assuming zero soil evaporation and adopting parameterizations for rac and
ra" according to CM88. The values of rsc predicted by CM88, which are a function of incoming
radiation only and calibrated using measurements, obviously agree best with both directly
measured and inferred values. The formulations for soil moisture stress and response to air
humidity adopted by VB95 and D78 result in higher values for rsc. The crop resistance in
VB95 is higher than in D78, partially owing to the different choices for the minimum crop
resistance (Table 5.2). In spite of this difference, the canopy evaporation rates of the two
models are similar (Figure 5.8). In VB95 the surface humidity is considerably higher than the
humidity at the canopy surface in D78 during daytime, due to the uniform high skin layer
temperature.
Figure 5.8: Measured and simulated total latent heat flux density; * observations; D78;
VB95; CM88
176 date
Figure 5.9: Simulated soil evaporation; » observations;
D78; - - - VB95; CM88
173 174 date
176
Another reason for the difference in canopy evaporation between D78 and CM88 is
the difference in parameterization of net radiation absorbed by the vegetation (Figure 5.12).
5. An intercomparison of 3 SVAT'S 161
The exponential extinction formulation adopted by CM88 gives higher values for the energy
available to the canopy than the explicit solution of the separate soil and canopy energy
balances as modelled by D78. Hence, a higher canopy evaporation rate will be predicted by
CM88 when all other variables remain unchanged.
0.16
0.14
Figure 5.10: Simulated soil moisture content by D78 ( ) and VB95 (•••••) at levels as indicated Ç °-1 2
I E
2 % 0.10-
0.08
0.06
VB95layer4
. D78 layer 1
VB95layer3
VB95 layer 1 " 1 /
D78layer2
VB95layer2
171 172 173 174 175 176
lOOOObr
Figure 5.11: Simulated and observed values of the canopy resistance, rs
c; Observations are carried out using porometry (») and inferred from measured total latent heat flux density (D);
D78; = VB95; CM88
173 174 date
176
5.3 Discussion and conclusions
A comparison of three schemes for describing the exchange of momentum, heat and
water vapour at the atmosphere-surface interface for a sparse canopy surface shows a wide
range of predicted results. In particular predicted values of soil heat flux density and surface
evaporation vary widely.
162 Sparse canopy parameterizations for meteorological models
Figure 5.12: Amount of net radiation absorbed by canopy layer parameterized by D78 and CM88;
D78; CM88
With respect to the soil heat flux density, the parameterization of D78 gives the best
results compared with data. The simple resistance approach of CM88 underestimates the soil
heat flux density by almost an order of magnitude, due to neglecting dynamic heat storage
in the upper soil layer. A dynamic heat storage, AG, can be implemented in the model of
CM88, while solving the temperatures at the surface and at the interface between the two soil
layers, at depth Zj. The heat necessary to change the temperature of the upper soil layer
could be considered simply by assuming that the temperature of the top soil layer changes
uniformly with depth during the simulation time step. This approach is similar to the
computation of the heat storage in a well-mixed water reservoir (see Keijman, 1974).
However, the effect of AG on the total soil heat flux density strongly depends on the choice
for Zj, since the well-mixed criterion is used. In a real soil this criterion is never met, and a
good estimate of G will only be achieved by a smart choice for Zj, without the possibility for
providing a universal solution.
VB95 also underestimates soil heat flux density, by approximately 30%. Much of this
underestimation is due to the choice of the value for the apparent heat conductivity of the
skin layer, A. For a dense canopy, the presence of the vegetation will thermally isolate the
soil from the atmosphere, and A may be expected to be small. For a sparse canopy, however,
this temperature difference can be regarded as proportional to the soil temperature gradient
immediately below the surface. Obviously, a value of A could be chosen corresponding to
the soil type under investigation which would give a better prediction of G. A value of 17
rather than 7 W/m2K would be a more appropriate estimate for A in the current situation
(section 4.1.3).
In all tested models the surface temperature plays a key role, since it regulates
important processes such as soil heat flux, sensible and latent heat flux, and net radiation.
CM88 predicts high sensible heat fluxes in the original form, since surface temperatures are
strongly overestimated when too little heat is transported into the soil. However, when the
soil heat flux density was forced to values simulated by D78, their parameterization of the
aerodynamic exchange within the canopy (using the resistance labelled ras) appeared to give
better results of the surface temperature than the formulation used by D78. In CM88, the total
exchange resistance for heat between the bare soil and the reference level resembles the
value included in VB95, which was based on field measurements of roughness length,
surface temperature and sensible heat flux. D78 prescribes a value of ras which is about half
5. An intercomparison of 3 SVAT's 163
as high as CM88, and consequently underestimates the bare soil temperature. Note that r s as
parameterized according to eq. 4.58 depends on the choice of zR, taken 2.95 m here.
The parameterization of aerodynamic transfer of heat is especially important for a
sparse canopy like the vineyard under investigation, where during daytime high sensible
heat fluxes from the bare ground component occurred. The heat transfer is dominated by
the soil component, but it is governed by many meteorological parameters in the
partitioning of available energy between the soil and the vegetation. From the current
exercise it can be seen that when the aerodynamic transfer between the atmosphere and a
sparsely vegetated surface is treated as an excess resistance for heat, its value cannot be
expected to be constant, as was discussed earlier by Kustas et al. (1989), Verhoef (1995) and
Blyth and Dolman (1995). However, for the limited simulation period investigated in this
study a constant value of z0m/zoh = 200 as applied in VB95 yields satisfactory results with
respect to both surface temperature and sensible heat flux density.
The crop resistance for evaporation is best described by CM88, where a calibrated
function of incoming radiation was used to describe rsc. The dependence of rf on soil
moisture content cannot be expected to be realistically described by either D78 or VB95,
which assume a much smaller root zone than found in our field. Also the response of
stomatal aperture to ambient humidity deficit is not fully resolved, and is an issue of
discussion. Under dry and warm conditions several plant species seem to develop a specific
survival mechanism, and respond differently to air humidity than plants from which the
expression of Noilhan and Planton (1989) was obtained (Monteith, 1995b).
The partition of radiant energy over the vegetation and the underlying substrate is
solved differently by CM88 (adopting radiant extinction) and D78 (solving separate energy
balances for the two surface components). The extinction parameterization was originally
developed for closed canopies, and is expected to deviate significantly from real radiative
interception for a vegetation stand with widely separated plants. On the other hand,
drawing up separate radiation balances does not take all edge effects into account. Which of
the parameterizations is to be preferred can only be supported by detailed measurements
and modelling efforts, and will most likely be different for each type of vegetation.
For large scale applications a land surface scheme necessarily needs to describe
accurately a wide range of land surface types, covering the full transition from densely
vegetated to completely bare. From the current study, a general conclusion can be made that
for a rather sparsely vegetated surface none of the three models compared can be regarded
to be the 'ideal' land surface scheme. Each of the schemes involved in this test has some
superior qualities compared to the others, but also shows significant deficiencies when
applied to a very sparse canopy. For the surface for which this comparison was run, a
combination of parts from each of the models will likely give optimal results. Following the
conclusions above such a combined model would consist of a soil heat flux parameterization
using the force restore method, an aerodynamic exchange process simulated using the
resistance formulation of CM88, and a canopy resistance parameterization that realistically
accounts for stomatal responses to soil moisture content and air humidity. Such a model will
be used as a reference in the next chapter, and will be outlined in more detail.
164 Sparse canopy parameterizations for meteorological models
6 Nature is alzvays numerically stable
Sensitivity of the planetary boundary layer to surface description
This chapter describes the influence of the description of the surface on the planetary
boundary layer. The issue of atmospheric sensitivity to the description of land surface
processes is not new (see, e.g., Garratt, 1993). Detailed studies were carried out previously
addressing PBL-sensitivity to surface albedo, roughness, crop resistance or soil moisture
content (Troen and Mahrt, 1986; McNaughton and Spriggs, 1986; Jacobs and de Bruin, 1992).
In these studies the value of one or more of the surface parameters was varied, and the
resulting range of predicted atmospheric variables was evaluated. Similar exercises were
carried out with land-surface parameterization schemes providing the lower boundary
conditions in GCM's (a list of these is included in the introduction section of this thesis).
By coupling land-surface models to larger scale atmospheric models, these studies
included the effect of atmospheric feedback, as outlined in chapter 1. Their focus was to
evaluate the sensitivity of the atmosphere to land-surface characteristics. They did so by
adopting rather extreme ranges of surface parameters, considered to describe the largest
possible atmospheric sensitivity to surface parameterization. For instance, the sensitivity
study of Charney et al. (1977) investigates the effect of changing the albedo for some areas
from 0.14 to 0.35. Jacobs and De Bruin (1992) and Sato et al. (1989) investigated the effect of
describing the surface evaporation by means of a (simple) biophysical model, instead of
using a simple bucket scheme.
The current study focuses on the response of the PBL to the physical parameterization
of the fluxes between the atmosphere and a specified surface, a sparse Mediterranean
canopy. The parameterization of surface fluxes from such a surface type has made
significant progress in the recent past. The main question that arises is the degree of
sophistication that needs to be included in the surface schemes, in order to obtain a realistic
description of the PBL dynamics. An optimum choice must be made between numerical
simplicity on one hand, and physical correctness on the other.
6. PBL-sensitivity to surface parameterization 165 •
The current study focuses on the manner of describing the surface processes
themselves, rather than changing values of specific surface parameters. The PBL-sensitivity
to different physical parameterizations of various surface processes is investigated, rather
than the effect of varying the surface coefficients. All included physical parameterizations
are designed to give a description of the surface exchange processes as realistic as possible,
using known characteristics of a specified surface. The parameterizations differ in
complexity or in theoretical foundation.
The strategy adopted here makes use of a coupled one-dimensional surface-PBL
model. Using the zero-dimensional comparison study, reported in the previous chapter, a
reference SVAT scheme is chosen. Next, the description of various components of this
reference SVAT are replaced with alternative parameterizations, and the effect of this
replacement on the computed state of the overlying PBL is the subject of analysis.
This strategy differs in two aspects from the zero-dimensional comparison study
presented in the previous section:
(1) instead of using atmospheric forcings measured at reference height, a coupled SVAT-PBL
model is used here. This allows description of the atmosphere-surface feedbacks,
which will affect the PBL-sensitivity to the surface description
(2) a reference model is defined, and components of this model are exchanged. In the
previous section complete models were compared which differed from each other in
many aspects. By changing single surface model components only, an attempt is
made to disentangle the complex coupled processes simulated simultaneously in a
full surface scheme.
Obviously, the results of this approach will partly depend on the choice of reference
model, on the simulated surface, and on the calibration of the various SVAT components. The
coupling between various surface processes (for instance, the effect of soil heat flux on
surface temperature and consequently on soil evaporation) will be different for different
types of surfaces or different ways of representing surface processes. However, the
complexity of the process interactions makes a reduction of the total number of degrees of
freedom inevitable, and emphasis is put on a single sparse canopy surface. In order to
maintain a certain degree of generality of the sensitivity study, a number of the prescribed
surface parameters were varied in some cases.
The sensitivity study is carried out for two sets of forcings and initializations: a
synthetic set and a measured set. The synthetic dataset includes two initial PBL-profiles,
chosen to represent climate zones in which sparse canopies are often found: a dry Tropical
profile (DRY) and a more humid Mid Latitude Summer profile (MLS). DRY is considered to
represent Mediterranean conditions in the dry growing season. MLS is included to represent
conditions which may be considered typical for agricultural crops with incomplete
vegetation cover, early in the summer.
The measured set of initial profiles and forcings is obtained from measurements
taken during the EFEDA-I campaign in June 1991. This set of model calculations is included
in order to evaluate the ability of the coupled SVAT-PBL model to describe actually measured
data, and to evaluate the sensitivity of this description to the surface parameterization. It
also adds to the sensitivity study by adopting initial profiles showing a pronounced
• 166 Sparse canopy parameterizations for meteorological models
presence of a residual layer, which often occured during EFEDA. The initial profiles are
obtained from a radiosounding carried out by CNRM, and the geostrophic and radiative
forcing are taken from measured quantities. A control run with measured surface fluxes is
included to provide insight in the skill of the uncoupled PBL-scheme for the present case.
An 'honest' intercomparison of parameterizations can only be carried out when the
various schemes are calibrated to describe a similar surface. Due to the different theoretical
backgrounds of the included schemes, this is not always straightforward. In all cases the
surface schemes were calibrated using data described in earlier sections.
First a summary of the reference model and variations thereupon will be presented
in section 6.1. Also the calibration of the model components is outlined. Then the setup of
the sensitivity analysis using the artificial input is discussed (section 6.2). The results of this
analysis are presented separately for daytime (convective) conditions (section 6.3) and
nighttime (stable) conditions (section 6.4). The results-sections are followed by a model
comparison applied using measured data. For this last analysis a selection of an adequate
comparison period had to be made. This selection and the data used are presented in section
6.5. Section 6.6 concludes this sensitivity chapter.
Model specification
The scientific backgrounds of the surface model components were discussed before
(section 4.1). Here, a brief summary is given. In most cases the calibration of the models is
similar as in the previous chapter (Table 5.2). Where appropriate, additional commentary is
given. The numerical schemes used to solve the coupled models are discussed in
Appendix V.
6.1.1 The reference model
The sensitivity of the PBL to the surface paramaterization is basically a sensitivity to
simulated surface flux densities. Therefore, an appropriate selection criterion for a
parameterized lower boundary condition is to select a SVAT describing the observed fluxes
optimally. In the conclusions of the previous chapter it was suggested that, using measured
forcings, the surface fluxes were optimally simulated by the Deardorff model, where
aerodynamic resistances were parameterized according to Choudhury and Monteith (1988),
and a realistic crop resistance was included. Verhoef (1995) tested a SVAT of this kind for a
Sahelian savanna and tigerbush surface. The reference model consists of the following parts
(see Table 6.1 for a summary):
• surface components: two surface components are distinguished: the canopy elements
and the underlying soil. A relative fraction of surface covered with vegetation is used
for calculating energy fluxes of each of these components. Each component is
allowed to obtain its own temperature and surface humidity.
• soil temperature: the force-restore method (eq. 4.47) is used to describe the soil surface
temperature Ts. Basic parameters determining the temperature change of the top soil
layer are the specific heat of the soil, the temperature of the lowest layer (assumed to
vary according to an annual wave) and the soil heat flux density.
• net radiation: shortwave and longwave incoming radiation are specified. Net- i
6. PBL-sensitivily to surface parameterization 1 6 7 •
radiation for each surface component is obtained by using its temperature to specify
emitted longwave radiation. Albedo and longwave emissivity are specified
coefficients. In contrast to the simulations in chapter 5, the longwave emissivity of
the plants was taken to be 0.90 rather than 0.98.
• surface fluxes: canopy evaporation is calculated by defining a fraction of the potential
evaporation using the ratio of leaf stomatal and leaf boundary layer resistances. Soil
evaporation is parameterized by specifying a relative humidity of the soil surface, as
function of the soil moisture content of the top soil layer. Soil heat flux is the
remainder of the energy balance at the soil.
• aerodynamic exchange: the aerodynamic resistances are calculated following
Choudhury and Monteith (1988). The resistance above the canopy is similar for
momentum and heat. Bulk boundary layer and within-canopy aerodynamic
resistance are functions of leaf area index, roughness length of the soil, and surface
roughness and displacement height. Measured values of z ^ and d were used instead
of the canopy roughness characteristics calculated by Shaw and Pereira (1982).
• soil moisture: as for temperature, a two layer force-restore method is used. Soil
hydraulic properties are described as proposed by Clapp and Homberger (1978).
• canopy resistance: a simple scheme proposed by Choudhury and Monteith (1988) is
used, which describes rsc as function of LAI and total shortwave radiation only. The
response of rsc to shortwave radiation is calibrated using field data.
6.1.2 Model variations • The case 'big-leaf'
In the case 'big-leaf' the two-component surface source is replaced by a single 'big-
leaf' approach, in which the surface consists of a single source with uniform temperature.
The energy balance of the surface is solved with the incoming radiation terms specified. As
in the reference case the force restore-method is used to describe G, but this time the soil
heat flux is evaluated from a known value of the surface temperature, rather than the other
way round (eq. 4.8). The same lower boundary conditions in the soil apply as in the
reference case. An excess resistance for scalars is used, by taking z0m /zoh = 200. The surface
longwave emissivity was fixed at 0.98.
• The case 'isotherm'
In the case 'isotherm' the surface source consists of a single layer with a uniform
temperature, as in the big-leaf approach. However, various fractions are discerned with
respect to the evaporation rate: a skin reservoir with open water (filled with dew and
intercepted water), an evaporating plant canopy and an evaporating bare soil. The surface
description in this case resembles the treatment employed in the ECMWF-surface scheme
(Viterbo and Beljaars, 1995) and the model of Noilhan and Planton (1989). Net radiation,
sensible and soil heat flux density, and an excess resistance used to discern between
momentum and scalar transfer, are treated as in the case 'big leaf'.
• The case '3 fracs' The case '3 fracs' was included as to evaluate the effect of the temperature
• 168 Sparse canopy parameterizations for meteorological models
Table 6.1: Variations of the surface model
Variation code
reference
big leaf
isotherm
3 fracs
aero D78
aero MH95
r c C 0 2
rc VB95
rc fix
rc big C 0 2
soil VB95
soil r*
soil CM88
sources at surface
canopy and soil
big-leaf
VB95
VB95 (non isothermal)
big-leaf
CM88
partition of radiation
D78
-
-
-
SW85 (modified ext.coeff.)
aerodynamic exchange
CM88
excess resistance
excess resistance
excess resistance
D78
MH95
Louis (1979)
crop resistance
CM88 (calibrated)
assimilation
VB95
fixed
assimilation
soil heat and water fluxes
force-restore
VB95
XES using
CM88
remarks
d(û/dt and dT/dt from force-restore
Q. from reference, no iteration for r.'
differentiation in the VB95 model in a coupled mode (see section 4.1.3). The surface energy
balance is computed separately for each surface fraction (open water, canopy and bare
ground), and the final fluxes of XE, H, Q» and G as well as the temperature of the upper soil
layer and the aerodynamic resistances are computed by averaging the resulting quantities
weighted by the appropriate surface fractions (eq. 4.18).
• The case 'aero D78' The aerodynamic resistance within the canopy, computed assuming an exponential
decay of the eddy-diffusivity, is replaced by a simple drag partition scheme proposed by
Deardorff (1978) in the case 'aero D78'. An effective canopy wind is obtained by
interpolation between the reference wind and «», and an iterative stability correction is
applied. For consistency with results reported in section 5.2.2, in the coupled surface layer-
PBL models ras is evaluated using eq. 4.58, in which ua and CH are evaluated at a height of 2
m above the canopy top (that is, at 3 m for the EFEDA sparse vineyard canopy). Also the leaf
boundary resistance is treated simpler than in the reference model, by not taking wind
speed gradients within the canopy into account.
6. PBL-sensitivity to surface parameterization 169
• The case 'aero MH95'
In the case 'aero MH95' the aerodynamic resistances both within and above the
canopy defined by Choudhury and Monteith are replaced by the resistances proposed by
McNaughton and Van den Hurk (1995), which are based on Lagrangian principles (see
section 3.2.3). The values are chosen to represent a uniform source profile (Beta-distribution
with p = q = 1), the value of cw/ut at z = 0 equal to 0.15, and the wind profile extinction
coefficient au equal to 3 (see Tables 3.2 and 3.3). For the normalized near-field resistor 5Rn the
suggested value of 0.36 was applied. Note that the value of the normalized aerodynamic
resistance above the canopy corresponds to a reference height of 2h. The resistance was
extrapolated to the reference level zR according to
^(zR) ^%l(2h)+ I In \ J
(6.1)
Actual resistances were obtained by dividing the normalized values by u,. Values of u, were
obtained from ua by using the Dyer-Hicks stability corrections for the pathway between zR
and 2h (see Appendix V).
• The case 'rc C 0 2 '
The case 'rc C 0 2 ' replaces the parameterization of the crop resistance by the
assimilation routine of Jacobs (1994), scaled up to the canopy level (section 3.4).
• The case 'rc VB95'
In the case 'rc VB95' the crop resistance is described by the multiregression model of
Viterbo and Beljaars (1995). In this model, the crop resistance is only affected by the
shortwave radiation and soil moisture (see eqs. 4.26 - 4.28). No dependence on ambient
humidity deficit is included. The calibration is carried out according to the suggestions
made by VB95. For öä the value of K>2 ls used.
• The case 'rc fix'
In the case 'r fix' the crop resistance is replaced by a fixed value, independent of any
meteorological condition. This value is obtained using a weighted average of a diurnal cycle
of values of /•ƒ simulated in the reference model.
• The case 'rc big C0 2 '
As in the case 'rc C0 2 ' the assimilation routine of Jacobs (1994) and discussed in
section 3.4 is used to describe the surface resistance, but this time the surface model is
replaced by the big-leaf scheme (case "big-leaf). This case is included to demonstrate the
effect of a surface resistance with a strong response to environmental conditions.
• The case 'soil VB95'
The 'soil VB95' case is dedicated to the exploration of the effect of replacing the force-
restore method in the reference case by the 4-layer soil model as used in the ECMWF-surface
model (VB95). In this approach the variation of the soil temperature and soil moisture
• 170 Sparse canopy parameterizations for meteorological models
content are solved for four layers, using a numerical solution of a set of diffusion equations.
Thermal and hydraulic conductivity depend on soil type and moisture content, and are
parameterized with similar relations as in the reference model. The soil heat flux and soil
evaporation forcing the temperature and moisture changes are treated as in the reference
model. A zero heat flux and free water drainage are imposed as lower boundary conditions,
and the total simulation depth is taken equal to the original ECMWF land surface scheme,
that is, 2.89 m (see Table 6.7). In the VB95 model, the surface temperature forcing of the soil
volume is situated in a skin layer without heat capacity (section 4.1.2). For large soil heat
fluxes, a considerable temperature difference may occur between this skin layer and the
centre of the upper slab, at depth 3.5 cm. In order to employ a proper coupling between the
surface energy balance and the soil heat flux here, a very thin slab (1 mm) is added on top of
the diffusion scheme. The temperature of this slab is considered to be equal to the skin
temperature, from which net radiation and sensible heat flux are calculated. The soil
moisture transport is simulated with the original 4-layer diffusion scheme, and the thermal
soil properties of the upper thin layer are evaluated using the soil moisture content of the
upper slab of 7 cm depth. Water extracted by vegetation is taken from the upper three layers
only. As in the reference model, soil surface relative humidity is calculated by using eq. 4.19
but with the layer coefficient lc set to 1.6, as suggested by VB95.
• The case 'soil rss'
The case 'soil rss' represents an alternative description of soil evaporation. The
relative humidity at the soil surface is calculated according to the formulation of Philip
(1957, eq. 4.83). The marrie potential \|/ is obtained from the soil moisture content in the top
layer, using the Clapp and Hornberger (1978) parameterization, given by
¥ j = V, sat a>MJ
(6.2)
A soil evaporation resistance, rss, is included in the pathway of water vapour from the
surface to the canopy airstream. We used a fixed value of 2000 s/m, as suggested by
Shuttleworth and Wallace (1985) for dry soils. This value is close to the high-end of the
range span by the clear diurnal course reported by Van de Griend and Owe (1994), who
measured r$s of the EFEDA test site using a respiration chamber. Soil moisture transport is
treated similarly as in the reference case, that is, using a force-restore method.
• The case 'soil CM88'
In the case 'soil CM88' the soil heat flux is computed using the scheme of Choudhury
and Monteith (1988), that is, using a heat exchange resistance and a temperature difference
between the surface and an intermediate level under the surface. Also soil evaporation is
treated using a resistance formulation, as by CM88. The change of the deep soil temperature
is calculated as in the reference model. Also the soil moisture content of the two layers are
computed using the force-restore algorithm, in spite of the CM88-assumption that the lowest
soil layer is water-saturated. The depth of the upper soil layer is initialized at 0.1 m, and
changes as soil evaporation proceeds.
6. PBL-sensitivity to surface parameterization 171 •
In CM88, the computation of the soil heat flux density and soil evaporation are
imbedded in a rather complicated set of equations. These equations solve the temperature
and humidity at the bare soil surface, the canopy surface, the airstream within the canopy
and at the layer intersection within the soil, as well as the fluxes of water vapour and heat in
between these levels (see section 4.1.5). For the 'soil CM88' case the entire CM88 algorithm
replaces the D78 surface model. As discussed before (section 4.1.5), the two-layer canopy
models based on the Penman-Monteith concept suffer from numerical instability when
stability corrections are incorporated or when net radiation and soil heat flux are
parameterized as function of the canopy or soil temperature. Therefore, net radiation is
taken from the reference simulations. Its partition over soil and canopy is computed by
using the exponential extinction (eq. 4.65), with an extinction coeffient ßr set to 0.45. This
value results in a partition nearly similar to the reference model. The parameterization of the
aerodynamic resistance above the surface is carried out using the non-iterative scheme of
Louis (1979), in order to minimize numerical stability problems. In this way a steady state
solution of the surface energy balance is obtained, which is a consequence of replacing the
force-restore method by the CM88 strategy. The flux densities above the ground are affected
by the alternative prediction of the surface temperature, but their computation follows
practically the same physical treatment as in the reference model.
Table 6.2: Configuration of comparison groups. Also given are code letters and numbers for the surface models and surface types, respectively, for later reference
group surface models model surface types surface code code
surface reference a sparse vineyard canopy 1 representation case 'big-leaf' b sparse vineyard canopy oy = 0.4 2
case 'isotherm' c sparse vineyard canopy Cy = 0.7 3 case '3 fracs' d sparse vineyard canopy o, = 1.0 4
soil heat and water reference a sparse vineyard canopy on sandy loam 1 flux case 'soil VB95' 1 sparse vineyard canopy on sandy clay 5
case 'soil CM88' m case 'soil r s n
aerodynamic reference a sparse vineyard canopy 1 exchange case 'aero D78' e tigerbush 6
case 'aero MH95' g forest 7
canopy resistance reference a sparse vineyard canopy 1 case 'r C02 ' h case 'rc VB95' i case 'r fix' j case 'rr big CQ2' k
6.2 Set-up of the sensitivity analysis
6.2.1 Basic strategy
Many of the surface processes show complex interactions. An investigation of all
possible combinations of selected model variations, initializations and surface land types
may seem appropriate since it will include all these interactions, but in practice is not useful
due to the large amount of quantities that must then be evaluated. Therefore, a set of four
172 Sparse canopy parameterizations for meteorological models
relevant groups of parameterizations were defined, and separately discussed: a source
representation group, a soil heat and water flux group, an aerodynamic exchange group, and a
canopy resistance group. Each of these groups contains a number of model combinations and
land surface types. A 36 hour run with a coupled surface-PBL model is carried out for each of
the relevant surface types using a prescribed radiative forcing. Two different initial PBL-
profiles are taken for each of the runs. First the four different groups containing the model
combinations and land surface types will be briefly discussed. Table 6.2 summarizes the
layout of the various groups. The next sections pay attention to the definition of the
evaluated SL- and PBL-parameters, and to the forcing and initial profiles adopted in the
simulation runs.
The source representation group is designed to evaluate the importance of recognizing
separate sources of heat and water vapour in case of a sparse canopy surface. For that
purpose, four different surface model combinations are included: the reference model, and
the cases 'big-leaf', 'isotherm' and '3 fracs'. The surface is parameterized as a sparse
vineyard canopy as encountered during the EFEDA experiment. Parameter values for this
default surface are found in Table 6.3. Furthermore, a range of degrees of vegetation
coverage is allowed, ranging from 0.11 (the default value) to 1.0.
Table 6.3: Default parameter values for sparse vineyard canopy. Only listed are the parameters which are changed in the sensitivity analysis. Remaining surface parameter values can be found in Table 5.2.
parameter
Leaf Area Index per unit plant surface
roughness length momentum
roughness length scalars (for one-layer
cases)
displacement height
crop height
fraction vegetation cover
soil type
reference
symbol
LAI,
z0m
z0h
d
h
°f
vineyard
3 m2/m2
0.04 m
2om/200 m
0.45 m
l m
0.11
this study
value
tigerbush
3 m2/m2
0.44 m
W 2 0 0
2.00 m
4 m
0.33
forest
3 m2/m2
0.40 m
W 2 0 0
5.10 m
8m
0.25
sandy loam (see Table 6.4)
Dolman et al., 1992
Garratt, 1978
The soi'/ heat and water flux group pays attention to the effect of various parameteri
zations of soil heat flux and soil evaporation. Again four different model combinations are
included: the reference model and the cases 'soil VB95', 'soil CM88' and 'soil rss'. The inter-
comparison is carried out for a sparse vineyard canopy on two different types of soil: the
default sandy loam, and a denser sandy clay soil. Parameter values of these soil types can be
found in Table 6.4.
The aerodynamic exchange group investigates the different parameterizations of the
aerodynamic resistances in the two-component model. Three different cases are compared
here: the reference model, and the cases 'aero D78' and 'aero MH95'. The sensitivity analysis
is carried out for three different vegetation types: the default sparse vineyard canopy, a
6. PBL-sensitivity to surface parameterization 173
Table 6.4: Soil parameters for different soil
soil type
sandy loam
sandy clay
Vsat (m)
-0.25
-0.15
b a
4.9 0.219
10.4 0.139
P
4
8
types
C2ref
1.8
0.3
"•sat (m/s)
3.41 10'5
2.15 10'6
°>sat (nrVm3)
0.472
0.426
(m3 /m3)
0.075
0.075
ay, ( - a>c) (m3 /m3)
0.354
0.320
sparse tigerbush vegetation in semi-arid areas (Dolman et al., 1992) and a moderately dense
forest canopy (Garratt, 1978). Aerodynamic parameter values for these surface types can be
found in Table 6.3.
The canopy resistance group explores different canopy resistance models with varying
complexity. In this group five different canopy resistance parameterizations are included.
The reference model includes a dependence of rsc on LAI and shortwave radiation only (the
calibrated simple formulation of CM88). The case 'rc VB95' adopts also a dependence on soil
moisture content. 'rc C 0 2 ' and 'rc big C0 2 ' are treated using the photosynthesis model, and
include dependences on ambient humidity deficit, radiation and leaf temperature. The last
case, 'rc fix' excludes any dependence by treating rf as a fixed parameter. The practical
formulation of the canopy resistance is usually carried out by using an extensive species
specific calibration. Many species could be investigated and included in the surface
description. However, to serve simplicity and comparability with other parts of this study
the work is confined to the default sparse vineyard canopy. For the two photosynthesis
models (cases 'r C 0 2 ' and 'r big C02 ' ) the calibration coefficients as found by Jacobs (1994)
were adopted (see section 3.4). Table 6.5 lists the relevant coefficient values for the resistance
models.
6.2.2 Specification of considered SL- and PBL-parameters The coupled SVAT-PBL model used for this study was designed to describe diurnal
variations of energy and momentum fluxes. As a result, the PBL-temperature, humidity
content and height vary with time.
In order to quantify the PBL-sensitivity to the surface parameterization a set of
relevant parameters must be specified which allows an objective intercomparison of the
various model components. Furthermore, we are interested in differences between the
effects of various model components on these parameters, compared to a specified reference
set of model components. Therefore, a sensitivity of parameter x to the surface
parameterization is defined as
_*K)-*K) (63) x x(mr)
where x(m^ is the PBL-parameter computed with model variation m(-, and mr is the reference
model variation. For the parameters indicating a temperature or specific humidity a
sensitivity as expressed by eq. 6.3 is not very meaningful, and these are expressed as an
absolute difference with the value computed by the reference model. For an evaluation of
absolute values of x(m^, Appendix VI lists the values of x calculated with the reference model.
• 174 Sparse canopy parameterizations for meteorological models
Table 6.5: Coefficient values for the various canopy resistance models
model
reference (CM88)
photosynthesis
(cases 'rc C02 ' \ big C02')
'rc VB95'
'rr fix'
model
and
coefficient
cuticular conductance
change of conductance per unit shortwave radiation
radiation extinction coefficient
maximum humidity deficit
slope of Cj/Cs with changing humidity deficit
maximum Ct/Cs
plant type
minimum stomatal resistance
maximum stomatal resistance
shortwave radiation coefficients
fixed value of stomatal resistance
symbol
Scut
Si
ßr
max
So
ƒ
C3
s,min
r s,max
"2
"3
'«
value
0.0005 m/s
4 10'6 m/s / W/m2
0.7
58.2 g/kg
0.916
0.85
240 s/m
5000 s/m
0.19 1128 W/m2
30.8 W/m2
500 s/m
Values of physiological parameters for C3 plants can be found in section 3.4 and Appendix IV
The choice of the relevant parameters must reflect the basic physical characteristics of
the surface-PBL system. For daytime conditions the selected parameters are the surface
energy balance components (Q», H, XE and G) and amounts of entrained sensible and latent
heat during daytime, the mixed layer temperature, -specific humidity, -wind speed and
-height, and the change of the total soil moisture content in the soil simulation volume. In
order to avoid a tedious and unorganized intercomparison some data reduction is desirable.
Energy balance parameters as well as entrained heat fluxes are averaged to daytime (6 -18
GMT) and nighttime (18 - 6 GMT) values. Parameters describing the state of the PBL and the
change of the bulk soil moisture content are evaluated at fixed simulation time intervals.
Since the fluxes of sensible and latent heat were very small during the nighttime
simulations, a relative difference of these quantities is not very meaningful. Instead, for
discussion of the nighttime simulations we selected the minimum temperature at reference
height as a characteristic parameter, which is strongly associated with the nighttime cooling
due to forced convection and the initial temperature profile when the night begins. The
associated parameters that are presented are the specific humidity at the same reference
level, and the PBL-height, all at the same time where the minimum reference temperature
was recorded (around sunrise). Table 6.6 summarizes the chosen parameters.
6.2.3 Radiative forcings and initial profiles The simulations all started at 4 GMT for a hypothetical DOY 174, and were executed
for 36 hours with a time step At of 3 minutes. The shortwave radiative forcing was expressed
as a function of zenith angle Ç using the semi-empirical turbidity formulation (Holtslag and
Van Ulden, 1983)
6. PBL-sensitivity to surface parameterization 175 •
K* = 1041 cosÇ - 69 (6.4)
The incoming longwave radiation is parameterized using the formulation of Brutsaert
(1982):
ll = *a°t - !'24 (P V/7
J", \ J
o f (6.5)
with ea expressed in hPa and Ta in Kelvin. In these synthetic cases the radiative forcing (both
shortwave and longwave) were parameterized assuming the absence of clouds.
Table 6.6: Basic PBL-surface parameters included in the sensitivity analysis
Parameter
daytime net radiation
daytime sensible heat flux
daytime latent heat flux
daytime soil heat flux
daytime entrained sensible heat flux
daytime entrained latent heat flux
boundary layer height at 6 hours intervals
symbol
Q.D
HD
XED
GD
HP
XEtD
V
defined as
average Q, between t = 6 GMT and t = 18 GMT (day 174)
asQ.D
asQ,D
asQ.D
asQ.D
asQ,D
z, at f = 12, 18 GMT (day 174) and ( = 6 GMT (day 175)
soil moisture change compared to 6 GMT, day 174
PBL-potential virtual temperature at 6 hours intervals
PBL-specific humidity at 6 hours intervals
minimum nighttime reference temperature
minimum nighttime reference specific humidity
D [ I cOjfO - 1 (0,(0)] for t = 18 GMT (day 174 and 175) *
average 6„(t, z) between 0.1 zi and 0.9 z,, for t = 18 GMT (day 174)
a s e B '
minimum value of 80(zR) between t = 0 and 6 GMT, day 175
q(zR) at the same time as 8„mm
D is the depth of the lowest soil moisture layer in the model's soil simulation volume
The first of the two artificial initial PBL profiles, labeled Mid Latitude Summer (MLS),
was taken from Ellingson et al. (1991), both for Qv and q. They used and listed standard
atmospheric profiles derived by McClatchey et al. (1971) to intercompare longwave radiation
codes in climate models. The second profile, labeled DRY, was inspired on the EFEDA-I
radiosoundings of CNRM. The 60-profiles measured early in the season very much resembled
the so-called Tropical profile presented by Ellingson et al. (1991), shown in Figure 6.1.
However, as an example of (^-profiles observed later during the campaign, the profile of 23
June (DOY 174) 1991, 4:10 GMT is also shown in Figure 6.1. A clear residual layer is present in
176 Sparse canopy parameterizations for meteorological models
the profile of Qv. The exact shape of this profile was shown to have many appearances in the
later EFEDA-season. For reasons of representativeness, the Tropical G^-profile was chosen for
the DRY profile. However, the associated humidity profile, shown by the dashed curve in the
right panel of Figure 6.1, was very humid compared to the conditions encountered during
EFEDA. Therefore, for the DRY humidity profile a 'representative' artificial humidity profile,
based on several observed humidity profiles taken during the entire EFEDA season, was
drawn by eye. The typical shape of this artificial profile is clearly present in the observations
of 23 June, shown also.
For the calculations, only profile levels below z = 5 km were considered, and the
vertical resolution of the model was nearly corresponding to the resolution of the
observations taken during EFEDA. A small number of data points were omitted, and a total
number of 82 model levels was left, the lowest being at zR = 25 m. The grid box size
increased further from 25 m in the lowest part of the model to 85 m near the top.
In all cases the air pressure at the surface was kept at standard pressure (1013.5 hPa).
The geostrophic forcing was provided by assuming a constant geostrophic wind of 5 m / s .
The horizontal wind speed was kept at a constant (geostrophic) value for z > 1000 m, and
was extrapolated to the surface according to a neutral logarithmic profile. Also an initial
profile of the C 0 2 concentration was specified, affected by the cases where an active source
or sink of C 0 2 was modelled, that is, in the cases 'rc C0 2 ' and 'rc big C0 2 ' . An initial value
of 340 ppm at all levels was specified.
4000
300oj
2000-
1000
0 ' f-/ £~ '
V 1/
1 1 1
30 35 e v(oC)
Figure 6.1: Initial profiles of 6^ (left) and a (right); : MLS, taken from Ellingson et al. (1991) for both 8„ and a, and ——: DRY, taken from the Tropical profile of Ellingson et al. (1991) for 8,, and drawn by eye for a. Also shown are the measured profiles of 23 June 1991, 4:10 GMT (••••) and the Tropical humidity profile presented by Ellingson et al. (1991) (- - - )
An initial soil temperature and moisture profile were obtained from EFEDA-I field
measurements, taken at DOY 174,4:00 GMT. These values were used for all initializations, and
can be found in Table 6.7.
Results of the sensitivity analysis for daytime conditions
Only the simulation results for the first daytime period (6:00 - 18:00 GMT) are
presented here. A separate subsection (6.3.5) summarizes the sensitivity results for
6. PBL-sensitivity to surface parameterization 177
Table 6.7: Initial soil moisture and temperature profiles
depth (m)
all models except case
0 - 0.10 *
0 - 0.60 *
soil model case
0 - 0.001 "
0.001 - 0.07
0.07 - 0.28
0.28 -1.00
1.00 - 2.89
'soil VB95'
'soil VB95'
temperature (°C)
15.8
24.0
15.8
21.3
26.1
24.0
24.0
moisture content (m 3 /m 3)
0.07
0.15
0.07
0.08
0.15
0.15
these soil depths apply to the moisture budget only; the depths for the thermal force-restore method are equal to the depth of the diurnal and annual temperature wave, respectively (section 4.1.4) the upper soil layer only applies to the temperature diffusion; soil moisture in that layer is equal to the soil moisture in the second soil layer, and not computed separately
convective conditions, by comparison of all model simulations with a simple slab-model,
which is partly analytical.
6.3.1 The surface representation group The surface representation group contains runs from the cases 'reference', 'big leaf',
'isotherm' and '3 fracs', simulating vineyard canopies with oy equal to 0.11, 0.4, 0.7 and 1.0,
and initialized with DRY and MLS profiles (see Table 6.2).
100-
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
Figure 6.2: Differences in predicted daytime evaporation, WP, for the cases 'big leaf', 'isotherm' and '3 fracs' relative to the reference model. The fraction of vegetation cover oy varied between 0.1 and 1.0
• Surface parameters The most pronounced effect of treating the surface as a single isothermal source of
heat and water vapour is the prediction of the average daytime evaporation, XE (Figure
178 Sparse canopy parameterizations for meteorological models
6.2). The case 'big leaf' clearly results in a significant increase of XE , and this effect is most
pronounced when when oy is small. For larger amounts of vegetation cover the difference
between the two-component model and the big-leaf approach decreases, and the average
surface temperature driving the surface evaporation in the case 'big leaf' converges towards
the canopy temperature in the reference model. For oy = 1, almost no difference between the
two cases remains. Minor differences persist due to the different parameterization of the
aerodynamic resistances in the two models.
The initialization has a clear impact of the sensitivity of XE to the model choice: the
differences between case 'big leaf' and the reference are much larger for MLS than for DRY.
The same holds for the case 'isotherm'. However, from Figure 6.2 it is also obvious that the
latter case resembles the reference two-component model much more than the Tjig leaf' case.
The division of the surface into separate fractions with respect to evaporation reduces the
effect of the uniform surface temperature, which is approximately identical in both cases.
The reduction is caused by an artificial enhancement of the aerodynamic resistance in the
'isotherm' case. The surface evaporation for the case Trig leaf' is given by
£ = p (6.6)
while E in the case 'isotherm' (assuming a negligible evaporation from the skin reservoir) is
equal to
E = CyP + (1 - Cy) p (6.7)
°frs + Ta r"
For a zero soil evaporation (which applies to very dry top soil and can be obtained by taking a = <?fl/<7s«t(Ts))' e 1 - 6 7 r e d u c e s t 0
rs + rJ°f (6.8)
For small values of ra the cases 'isotherm' and 'big leaf' are nearly similar, and the total
evaporation is mainly regulated by the canopy resistance. However, owing to the relatively
large excess resistance included in ra, the cases differ significantly by the enhancement of ra
by a factor 1/oy.
When different temperatures for the different surface fractions are allowed (case '3
fracs'), the surface scheme simulates a lower evaporation than the reference model in all
cases. This reduction is less when cy increases.
The sensitivity of the total daytime sensible heat flux, H , to the surface
representation is shown in Figure 6.3. In all cases, the cooler surface temperature results in a
decrease of HD. The sensitivities are limited to 35% for the MLS initialization, and 25% for
DRY. The largest response of HD is generally not found in cases of almost bare soil or
complete vegetation cover, but occurs in between these limits. In spite of the large relative
difference of XED for cy = 0.1, the relative sensitivity of HD is small for all cases, due to the
6. PBL-sensitivity to surface parameterization 179 •
low absolute value of XE , and the consequently small redistribution of available energy towards H. For large values of oy the difference between the formulation of an average surface temperature by a single- or dual source model vanishes, and the impact of the surface representation on H° is consequently also small. The relatively high response of HD
for intermediate values of oy is the result of a balance of these two effects. The differences between the cases '3 fracs' and the reference model are mainly caused by a small phase shift of the simulated sensible heat flux, rather than different maximum values.
refe
renc
e (%
)
9 v
q
E
I"15" 8 s> te -20
•o <D •ê -25-JS £
-30-
-35
MLS
l l |
1 1 1 1
DRY
1 f
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
big leaf
isotherm
3fracs
Figure 6.3: As Figure 6.2, for daytime sensible heat flux, HD
big leaf
isotherm
3 fracs
Figure 6.4: As Figure 6.2, for the total daytime soil heat flux, G
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
The response of the daytime soil heat flux GD, shown in Figure 6.4, is somewhat different. The difference between the one-layer surface models and the reference are relatively small for oy < 1, but are generally higher for oy= 1. Common to all models that regard the surface as a single layer is the absence of simulating a sensible heat flux between the soil and the canopy. This tends to increase the soil heat flux. However, it must be noted
180 Sparse canopy parameterizations for meteorological models
that the absolute values of G calculated by the reference model are rather small: 42 and 49
W /m 2 for the MLS and DRY initializations, respectively (Appendix VI).
» "5
I ••! -10-
MLS DRY
n F
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
big leaf
isotherm
3 fracs
Figure 6.5: Boundary layer height at 18:00 GMT, 1st simulation day, for the cases explained in Figure 6.2
• Boundary layer parameters The effect of the surface representation on the boundary layer height at 18:00 GMT,
shown in Figure 6.5, follows roughly the pattern exhibited by the sensible heat flux response
(Figure 6.3). The PBL-height simulated by the reference model reaches approximately 1630 ±
60 m for MLS and 1520 ± 130 m for DRY. The close match between z,18 and HD is a direct
result of the small entrainment of heat (see below). The results of z™ at the next day show a
similar response (figures not shown), although the simulated PBL-heights are some 600 m or
so higher. A rapid PBL-growth is simulated in a near-neutral residual layer for the second
simulation day.
The entrainment of heat is fairly low in all cases. Both initializations result in a
daytime average heat entrainment of -5 W /m on the average. Due to the low absolute
values of HtD, relative differences are rather meaningless and not shown. Moisture is in all
cases transported out of the PBL rather than entrained into it, and the rate of this so-called
detrainment is strongly related to Cy. The different surface representations don't give rise to
large moisture detrainment differences for the MLS initialization, but a significantly higher
detrainment is simulated by the case 'big leaf' for an initial DRY-profile (Figure 6.6). The
strong surface evaporation results in a large moisture gradient across the top of the PBL (see
Figure 6.7), and this enhances the moisture flux. Owing to the steep humidity gradient
above the PBL (Figure 6.1), the compensating effect of a slightly lower PBL height is small.
This is not the case for the large humidity gradient in the MLS initialization. In spite of a
significant increase of PBL humidity (Figure 6.8), the entrainment is low. Here the small
reduction of z, resulted in a stronger reduction of the humidity gradient across the PBL-top,
as illustrated in Figure 6.7.
Apart from the cases where the surface evaporation is low (oy = 0.1), the response of
q18 (Figure 6.8) resembles the pattern of XED (Figure 6.2). The largest differences occur for
the case 'big leaf', where an increase of up to 1.2 g/kg is simulated.
6. PBl-sensitivity to surface parameterization 181
Finally, the impact of the surface representation on the mixed layer temperature at 18
GMT is very well explained from the differences in surface sensible heat flux, shown before.
The small entrainment of heat causes a fairly strict response of dv18 to HD (figure not
shown).
30-
20
10
-10-
-20-
-30-
MLS DRY
1 In.
nil
1 — i — i — i — i — — i —
P •
big leaf
isotherm
3 fracs
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
Figure 6.6: Differences in total daytime moisture entrainment, XEt
D, for the cases as shown in Figure 6.2
q(9"<g) q(g/kg)
Figure 6.7: Profiles of specific humidity simulated for oy = 0.1 by the reference case (solid lines) and the case 'big leaf' (dashed lines) for times 12:00 GMT (normal) and 18:00 GMT (thick); Left: MLS initialization; Right: DRY initialization. The dashed vertical lines in the left panel indicate the change of the humidity gradient across the PBL-top due to the change of zjß at 18:00 GMT. A similar change is not shown for the DRY simulation, since it very small
6.3.2 The soil heat and water vapour flux group In the soil heat and water vapour flux group four model variations are compared for
two soil types: sandy loam and sandy clay. The model variations include the cases
'reference', 'soil VB95', 'soil rf' and 'soil CM88'.
182 Sparse canopy parameterizations for meteorological models
-0.4 0.1 0.4 ' 0.7 ' 1.0
big leaf
isotherm
3 fracs
0.1 0.4 0.7 1.0 vegetation coverage
Figure 6.8: Absolute differences in mixed layer specific humidity at 18:00 GMT, <j™, for the surface and model variations as in Figure 6.2
• Surface parameters
The partition of net radiation over sensible, latent and soil heat is simulated rather
differently by the various model variations. Large differences are present for the simulation
of daytime soil heat flux (Figure 6.9). For both initializations the values of G predicted by
the case 'soil VB95' are approximately 40% lower than the reference case for sandy loam soil,
and 20% lower for sandy clay soil. Both the reference model and the case 'soil VB95' derive G
as a residual of the surface energy balance. They also adopted a similar lowest boundary
condition (no soil heat flux below the simulation volume), and equal physical expressions
for XT. In spite of this, the bare soil temperature is generally higher for 'soil VB95' than in the
reference case. This causes the sensible heat flux to be higher than for the reference model,
which has a negative feedback on the soil heat flux.
40-
20-
-20
-40
$ -60-
-80
-100
MLS DRY
P IT loam clay loam
soil type clay
soil vb95
soilrss
soilcm88
Figure 6.9: Differences in predicted total daytime soil heat flux, G , relative to the reference model, for the model cases 'soil VB95', 'soil rs
s' and 'soil CM88', for sandy loam and sandy clay soil types
6. PBl-sensitivity to surface parameterization 183
A major difference between the cases 'soil VB95' and 'reference' is also depicted in
Figure 6.10, where the total daytime surface evaporation is shown. For the sandy loam soil
type the two cases result in nearly identical amounts of evaporation, but for sandy clay the
reference model simulates 20% - 60% more evaporation than 'soil VB95'. One of the reasons
for this difference is the layer coefficient lc (eq. 4.19), equal to 1.0 for the reference model and
1.6 for the case 'soil VB95'. The coefficient efficiently reduces the surface relative humidity to
below the minimum level q0, for which soil evaporation is allowed. In the reference case this
reduction is not included, and a significant part of the total evaporation originates from the
bare soil component.
Figure 6.10: As Figure 6.9, for the daytime evaporation X.E
soil type
120-
Figure 6.11: As Figure 6.9, for the daytime sensible heat flux H
Also the cases 'soil rf' and 'soil CM88' simulate a lower surface evaporation for
sandy clay, the largest deviation of ± 60% present for 'soil rss'. For sandy loam, 'soil rs
s'
predicts an evaporation rate which is ± 60% higher than the reference model. The difference
184 Sparse canopy parameterizations for meteorological models
is entirely caused by an enhanced soil evaporation of 'soil rss'. In this model, two factors
regulate the soil evaporation: the soil resistance rss, and the relative humidity in the soil
pores close to the surface, given by eq. 4.83. This relative humidity is evaluated from the soil
moisture content in the top soil layer, which has a depth of 10 cm in the current simulations.
However, the soil moisture content shows a significant gradient close to the ground, and is
considerably lower in the top 1 cm than averaged over 10 cm. Van de Griend and Owe
(1994) report œ values of typically 0.02 m 3 /m 3 of the top 1 cm of the soil, measured at the
EFEDA-I test site. This is small compared to the initial value of 0.07 m 3 /m 3 , as adopted for
the simulations (Table 6.7). Furthermore, Kondo et al. (1992) point out that eq. 4.83 is invalid
close to the surface. An equilibrium situation, as assumed by Philips (1957) equation, is
violated near the surface due to evaporation. This also leads to an overestimation of the
surface relative humidity by case 'soil rf'.
The soil heat flux is nearly similar for both the reference model and the case 'soil r$s'
(Figure 6.9). The resistance formulation merely affects the surface evaporation, which is only
a minor part of the surface energy balance here. Similar arguments can be put forward for
the total daytime sensible heat flux (Figure 6.11).
The extremely low value of G as simulated by the case 'soil CM88' was noticed
before already (section 5.2.1). The effects of this low soil heat flux on the sensible heat flux
(Figure 6.11) is evidently large. Up to 100% more sensible heat (DRY-initialization, sandy
clay) is released into the atmosphere compared to the reference model.
• Boundary layer parameters
The high sensible heat fluxes simulated by the case 'soil CM88' have a major effect on
the PBL-height. Also the mixed layer temperature is significantly enhanced (Figure 6.12). For
the cases 'soil VB95' and 'soil rj" the increase of Qv18 is limited to ± 0.8 K, but 'soil CM88'
results in an increase of 1.5 - 2.5 K in all cases. As before, the coupling between differences in
Qv18 and z; to differences in H is strong, due to the low amounts of entrained heat.
Figure 6.12: (left:) Relative differences in predictions of PBL-height; (right:) Absolute differences in predictions of mixed layer temperature at 18:00 GMT for the soil types and model cases as in Figure 6.9
The effects of the strong evaporation rate for sandy loam in the case 'soil rf', and the
weak evaporation in all cases for sandy clay, are shown in Figure 6.13, where the mixed
layer specific humidity is plotted. The dry simulations for sandy clay are shown evidently in
6. PBL-sensitivity to surface parameterization 185
this figure. More striking is the strong reduction of q18 for the case 'soil CM88' for both soil
types, where for sandy loam a slight increase of surface evaporation was predicted (Figure
6.10). The large boundary layer height, combined with an increase of the moisture
detrainment by 40 - 50% (Figure 6.13, MLS), together are responsible for this feature.
nia
4 iïf
soilvb95
soilrss
Figure 6.13: (left:) Mixed layer specific humidity, qls; (right:) Daytime moisture entrainment, XE,D
6.3.3 The aerodynamic exchange group The aerodynamic exchange group contains simulations over the reference vineyard
surface, a tigerbush and a forest. Simulations are carried out with the reference model and
by means of the variations 'aero D78' and 'aero MH95'.
30-
. 25
| 20
15
! 10
MLS DRY
1 vine bush forest vine bush forest
surface type
aerod78
aero mh95
Figure 6.14: Different predictions of daytime sensible heat flux, HD, compared to the reference model for the cases 'aero D78' and 'aero MH95', for various surface types
• Surface parameters The different parameterizations of the aerodynamic resistances particularly affect the
simulated total daytime sensible heat flux (Figure 6.14). The differences from the reference
model are different for both model variations, and generally increase as the canopy becomes
rougher and taller. For the case 'aero D78' a gradual increase of \ „ D is a result of the effect
of particularly à on the aerodynamic resistance within the canopy in the reference model,
186 Sparse canopy parameterizations for meteorological models
expressed by eq. 4.71. The zero-plane displacement has only a limited effect on the value of
ras in the case 'aero D78' (by way of the quantification of u,), and this resistance is much
smaller than in the reference model (typically 75% for the forest vegetation type). Also the
case 'aero MH95' simulates smaller aerodynamic resistances, but these are parameterized
independent on the surface roughness parameters. The difference between this case and the
reference model are therefore again dominated by the effect of z ^ and d on ras in the
reference model. Unlike the gradual increase of Z,HD from vineyard to forest using 'aero
D78', the case 'aero MH95' shows a minimum value of ^HD for the intermediately rough
tigerbush surface.
The differences in H are fully compensated by opposite differences in the daytime
soil heat flux (figures not shown): in all cases net radiation and evaporation were simulated
nearly similarly.
g
12
1fr
8-
6-
4-
2-
o- * -
MLS
-
1
DRY
If aerod78 EH aeromh95
vine bush forest vine bush forest surface type
Figure 6.15: Boundary layer height at 18:00 GMT for the same simulations as shown in Figure 6.14
• Boundary layer parameters
The different predictions of daytime sensible heat flux lead to a remarkable
difference in boundary layer height at 18:00 GMT (Figure 6.15). The behaviour of z(- is very
similar to the change in surface heat flux for the case 'aero D78'. However, for the case 'aero
MH95' Z- shows a much stronger response to variations in H . A similar picture is
presented in Figure 6.16, where the PBL temperature at 18:00 GMT is shown. The reason for
the discrepancy between HD and z, is the increased entrainment of heat, simulated by the
case 'aero MH95'. In the reference model the heat entrainment flux is typically -5 W / m , but
for the case 'aero MH95' it is up to five times as large, approximately -25 W/m 2 . This is
caused by a complex interaction of parameterizations in the coupled models. The low
aerodynamic resistances in 'aero MH95', and the absence of stability corrections in the range
below 2h, are associated with relatively large friction velocities near the surface (figures not
shown). An increase of a» results in an increase of the variance of the vertical velocity, w .
This reduces the countergradient correction \ , which increases the modified temperature
gradient used to calculate the vertical heat flux in eq. 4.85. Since during daytime u» is not a
6. PBL-sensitivity to surface parameterization 187
scaling parameter in the PBL eddy diffusivity, the vertical heat flux is increased at heights
where \ plays a significant role, that is, near the top of the PBL. As a result, the boundary
layer grows faster, particularly at early times after sunrise, and its temperature becomes
higher.
0.9
o.a
2-0.7-
§ 0.6 £ •g 0.5
I 0.4-
s o.a i ~° 0.2
0.1-
o-
MLS J - | DRY
I I 1 I
I I
aerod78
aero mh95
Figure 6.16: As Figure 6.14, for 8,,18
vine bush forest vine bush forest surface type
6.3.4 The canopy resistance group
In the canopy resistance group five different parameterizations are intercompared for
a 'standard' vineyard surface: the reference model (calibrated version of CM88), and the
cases 'rc C0 2 ' , 'rc VB95', 'rc fix' and 'r big C0 2 ' .
• Surface parameters
The parameter that is primarily affected by the parameterization of the canopy
resistance is the total daytime evaporation, shown in Figure 6.17. The case 'r C 0 2 ' yields a
total evaporation which is 80% higher than is computed by the reference model for the
relatively cool and moist MLS initialization. For DRY the difference is 40%. This behaviour in
fact shows the response of rf, as computed by the photosynthesis model, to ambient
humidity deficit: the MLS initialization puts a smaller constraint on the crop conductance
than a warmer and dry initial profile (DRY). The parameterizations embedded in the cases 'rc
VB95' and 'rc fix' give values of XE which are approximately 50% and 10% lower than the
reference, respectively. The close correspondence between case 'rc fix' and the reference
model is mainly due to the choice of the fixed value of rsc, being equal to the daily average
of the parameterization in the reference model. For the case 'rc VB95' a strong soil moisture
response is included in the parameterization of rsc, which results in relatively high values
owing to the low soil moisture content in the simulations.
The large reduction of the predicted daytime evaporation by case 'rc big C0 2 ' is
somewhat surprising, given the increases of XE by both cases 'big leaf' (Figure 6.2) and 'rc
C0 2 ' . The reason for the strong reduction of XE is the pronounced response to the ambient
humidity deficit, present in the photosynthesis model for rf. The high leaf temperature
— which is a consequence of the isothermal source description in a big leaf model — enforces
188 Sparse canopy parameterizations for meteorological models
a high ambient humidity deficit. This imposes a strong limitation to the canopy
conductance, thereby reducing the evaporation rate. The case 'r big C0 2 ' produces
relatively high evaporation rates just after sunrise and just before sunset, but the
evaporation rate during midday reduces to low values (figures not shown).
re big co2
Figure 6.17: Differences in predicted total daytime evaporation, XED, compared to the reference model, for the case 'rc
C02 ', 'rc VB95', rc fix' and 'r big C02 ', for the reference vineyard surface
vine vine surface type
surface type
Figure 6.18: (Left:) Daytime soil heat flux, GD; (Right:) Daytime sensible heat flux, HD, for cases as in Figure 6.17
The impact of the cases in the canopy resistance group on the other energy budget
terms is smaller: the soil heat flux changes by less than 5% in all cases. Changes in the
sensible heat flux are limited to 15% (for the case 'rc C 0 2 ' with the DRY initialization), and
tend to compensate most of the effects of r$c on XE (Figure 6.18).
• Boundary layer parameters
The effect of the choice for the computation algorithm for rf on the PBL height at
18:00 GMT follows closely the response of the daytime sensible heat. It is inversely
proportional to the computed latent heat totals. The effect of these two processes on the
6. PBL-sensitivity to surface parameterization 189
average specific humidity in the mixed layer is shown in Figure 6.19. As expected, a slight
increase is present for the 'rc C 0 2 ' cases.
Figure 6.19: As Figure 6.17, for the differences in PBL specific humidity, qls
A somewhat more unexpected picture is shown in Figure 6.20, where the differences
of the predicted total moisture entrainment compared to the reference are plotted. A 40%
increase of moisture detrainment is simulated by the case 'rc C0 2 ' , for DRY only. The
background of this increase is related to the timing of the simulated surface evaporation.
The case 'rc C 0 2 ' calculates the peak evaporation well before noon, which results in an early
rise of the specific humidity of the PBL. A larger difference between q and the specific
humidity of the free atmosphere above is present for this case than for the reference model.
This gradient enhances the simulated transport of moisture out of the PBL. The absolute
effect of this extra detrainment on q is relatively small.
rcco2
rcvt>95
rclix
40i
30
20
10
-10-
-20-
-30-
-40-
MLS 1 DRY
1 I J l l Figure 6.20: Differences in
^ H moisture daytime entrainment, rc big co2 XEt
D, for the same simulations as in Figure 6.17
vine vine surface type
190 Sparse canopy parameterizations for meteorological models
6.3.5 PBL-sensitivity and an analytical approach
The different surface parameterizations described above cover a considerable range
of predicted sensible and latent heat totals. Assuming that the collection of these surface
schemes represents the current state of the art of the parameterization of sparse canopy
surfaces, this range of surface energy totals can be regarded to span a likely range of PBL
predictions. A summary of the PBL-sensitivity can thus be obtained by plotting the most
relevant PBL-parameters as function of the surface energy budgets as computed by the
various surface models.
A similar sensitivity analysis was carried out by Driedonks (1981,1982b), using the
simple slab model of Tennekes (1973) (section 4.2.2). For the sensitivity of z; and 6m to the
integrated surface heat flux I, analytical expressions were developed. For the sensitivity of
qm to the integrated surface evaporation ƒ, no analytical expressions were derived, and the
value of cjm at 18:00 GMT was computed numerically with the slab model. Here we compare
the values of zi , 9m and qm as function of J and ƒ calculated with this simple slab model,
to the results of similar sensitivities as computed by the series of coupled SVAT-PBL models
described above. For comparison with the analytical model for the dynamics of the PBL-
temperature, the mixed layer temperature Q18 rather than the virtual temperature Qv18 is
obtained from the numerical simulations. The values of ö^,, q00, y e and y were obtained
for each of the initial profiles (Figure 6.1), and are listed in Table 6.8. In all cases Sp' and 80e
were taken zero, as the simulations started at the time where A9, Aq and zi0 were small.
Table 6.8: Values of QQQ, qm ye and y for the initial profiles labeled MLS and DRY
quantity
«oo (°Q
loo (g/kg)
Ye ("Cm"1)
y, (g/kg m1)
height range for determination y (m)
19.80
11.70
5.33 10"3
-2.85 IO"3
200 - 2000
25.66
4.34
4.08 10°
-2.10 10"4
200 - 2000
• PBL-height as function of surface heat flux
Figure 6.21 shows the values of zç plotted against the integrated daytime surface
virtual heat flux I, calculated as 12 x 3600 x H /pc , for all coupled SVAT-PBL simulations.
Also shown is the analytical expression (eq. 4.92), with entrainment coefficient values of 0.2
and 0.0. The datapoint labels refer to the model runs specified in Table 6.2 on page 172.
For both initializations the results from the coupled models show a consistent
increase of z,- with increasing I. At low values of I, z, reaches relatively high values,
compared to the predictions of the slab model. This is partly caused by an absence of the
effect of the virtual component on the entrainment flux, which is not included in the simple
slab model. Adopting an entrainment ratio of Rh = 0.2 results in a correspondence with the
numerical simulations at low values of I. For higher values of I, the analytical model
describes the coupled model runs slightly better for Rh = 0.0 than for Rh = 0.2. The simulated
daily averaged entrainment coefficients were in most cases equal to approximately 0.1,
which is consistent with the analytical expression. However, the entrainment ratios found
6. PBL-sensitivity to surface parameterization 191
here are rather low, and this will be discussed in section 6.6.
A few outliers are present. For the MLS profile gl, g6 and g7 (model case 'aero MH95')
show a higher PBL-height at 18 GMT than model combinations with comparable values of I.
The reason for this - higher values of friction velocity combined with enhanced heat
entrainment - was discussed above already, and causes a resemblance with the analytical
solution using Rh = 0.2 (figure not shown). For the DRY-inihalization only the datapoint
labelled gl shows a similar behaviour.
For the MLS initialization, dz{18/dl = 0.12 K"1 (estimated from Figure 6.21), while for
DRY this sensitivity is approximately equal to 0.15 K"1.
2500
2400
2200
2000
1800H
1HX)J
1400-
12001
won-
DRY
Vf*
y
± a>
'
A O D °
—
aP j."
A
ti
_
A
ss ™
Figure 6.21: PBL-height at 18:00 GMT plotted against integrated surface heat flux J for the 2 initializations MLS and DRY: G model cases; » analytical solution with Rh = 0.2; - analytical solution with Rh = 0.0. Labels refer to model cases and surface types explained in Table 6.2 on page 172
2000 5000 6000 I (Km)
• PBL-temperature as function of surface heat flux The relationship between Q18 and I, plotted in Figure 6.22, shows up as a nearly
straight line. The analytical expressions are particularly insensitive to the value of Rh. The
analytical solutions and the numerical model runs result in a nearly similar dependence of
Q18 on I, although the numerical models tend to be slightly less sensitive to I. Overall, the
sensitivity d&18/dl = 5.9 10"4 m"1 for MLS and 6.7 10"4 m"1 for DRY. Again, these sensitivities
were derived by eye from Figure 6.22.
192 Sparse canopy parameterizations for meteorological models
As for the sensitivity of zç to I, the model runs gl - g7 lie out of the range. The
enhanced entrainment due to the large mechanical contribution causes heating of the PBL,
which exceeds the heating rate expected from the surface contribution solely.
• PBL-humidity and surface water vapour flux
The numerical prediction for q using the slab model as function of the integrated
surface moisture flux, ƒ = 12 x 3600 x XE A p , is shown in Figure 6.23, together with the
simulations from the coupled models. The scatter for both models is larger than for the
former two relationships. In the slab model, the expression for q includes an independent
variable dz;/df, which is a function of I. This independent variable is not present in the
thermal relationships. Furthermore, the relative contribution of water vapour transport near
the top of the PBL is significant and of the same order as the surface evaporation.
Figure 6.22: As Figure 6.21, for the relationship between 918 and I
2000 3000 4000 5000 6000 7000 8000 9000 I (Km)
Clearly, q generally increases as ƒ increases, and the two models result in a similar 28/ response. A linear regression for all datapoints yields a sensitivity dq /dj equal to 8.12 10
m"1 for MLS, and 8.27 10"4 m"1 for DRY.
6. PBL-sensitivity to surface parameterization 193
Figure 6.23: As Figure 6.21, for the relationship between q and ƒ. The dashed lines show the linear regressions of q predicted by the combined models as function of ƒ
3500
6.4 Results of the sensitivity analysis for nighttime conditions
For nighttime conditions only a limited parameters is evaluated (see Table 6.2): the
minimum temperature at reference height (Qvmm), and the specific humidity at reference
height (qmln) and the boundary-layer height (z™™) at the same time.
6.4.1 The surface representation group For all simulations in the surface representation group, the minimum temperature at
reference height occurs just before sunrise (after ± 24 hours of simulation). For all
parameterizations in the surface representation group, Qvmm is considerably higher than for
the reference model (Figure 6.24). The reason for this difference is the parameterization of
the temperature at z ^ , which affects the stability correction in the aerodynamic resistance
between the surface and the reference level. Accounting for two separate surface sources, as
adopted in the reference model, generally yields lower values for 90 during nighttime. The
differences are particularly evident for a surface having an intermediate vegetation cover,
and temperature differences of up to 3.5 °C may be the result, as shown in Figure 6.24.
A large difference is also present for the specific humidity at reference level, just
194 Sparse canopy parameterizations for meteorological models
before sunrise (Figure 6.25). Here a pronounced influence of Oris present. The origin of the
different values of qmm differs from the origin for the temperature variability. Here, the
single layer models sustain a small evaporation during the night. This evaporated moisture
quickly becomes trapped in the very shallow boundary layer.
Figure 6.24: Differences of minimum nighttime temperature at reference level, 8v
mm for the model cases "big leaf', 'isotherm' and '3 fracs' compared to the reference model, for values of oy ranging between 0.1 and 1.0
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
Figure 6.25: As Figure 6.24, for the minimum reference specific humidity, tfin
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
The differences in aerodynamic resistances, noticed above, also have an impact on
the simulated friction velocity. This shows up in the simulations as a variation of the PBL-
height just before sunrise (Figure 6.26). However, since the absolute values of zi are rather
low (± 50 m), and the number of simulation layers within the nightime PBL is limited to 4 or
5, these relative figures are not very significant. The DRY simulations give rise to smaller
differences than MLS.
6.4.2 The soil heat and water vapour flux group
In the case 'soil rss' the bare soil temperature reaches a lower value than in the
6. PBL-sensitivity to surface parameterization 195
reference model for a clay soil. The result is a significantly lower air temperature just before
sunrise (Figure 6.27). For 'soil VB95' this is the case for the sandy clay soil type. In this figure
the results for case 'soil CM88' are omitted, since some meaningless values were simulated
here due to a lack of numerical stability.
Figure 6.26: As Figure 6.24, for the PBL-height at 6:00 GMT, zf
0.1 0.4 0.7 1.0 0.1 0.4 0.7 1.0 vegetation coverage
2- 0-
E -1 2 <D
MLS DRY
r n
loam clay
soil vb95
soilrss
loam soil type
clay
Figure 6.27: Difference of minimum temperature at reference height, e„mm, for model cases 'soil VB95' and 'soil rs
s', compared to the reference model
6.4.3 The aerodynamic exchange group
The observed temperature differences found above are less pronounced in the
aerodynamic exchange group (Figure 6.28). A cool reference temperature, simulated by case
'aero MH95', is evident for the DRY-initialization. The absence of a stability correction on the
aerodynamic resistances below z = zR plays a major role here. A significant reduction of the
wind speed gradient between z = zR and z = z0m is simulated by the case 'aero MH95', since
r a is hardly increased by a stability correction.
196 Sparse canopy parameterizations for meteorological models
Figure 6.28: Differences of the minimum reference temperature, Qjnm j o r jjjg mo<jei cases 'aero D78' and 'aero MH95' compared to the reference model, for various surface types
vine bush forest vine bush forest surface type
6.4.4 The canopy resistance group
The issue of the increased reference humidity shown in the surface representation
group is obviously also related to the parameterization of the canopy resistance: imposing a
nighttime value of r ' > will effectively remove all nighttime evaporation, and the
difference between the various surface models is likely to vanish. A significant difference
with the reference model is only present for the case 'rc fix', which adopts a lower canopy
resistance than any of the other cases (Figure 6.29).
eren
ce (g
/kg)
b
en
c
E g » 0.5-o c S
£ T3
MLS
.1 . 1
DRY
1 I
vine surface type
vine
rcco2 • rcvb95
rc fix
rcbigco2
Figure 6.29: Differences in predicted early morning specific humidity, qmm, for the cases 'rc
C0 2 ' , 'rc VB95', rc fix' and 'rc big C0 2 ' , compared to the reference model
Simulations using EFEDA-observations
The sensitivity analysis described above was carried out using rather idealized
radiative and geostrophic forcings and initial PBL-profiles. However, the measurements
carried out during the EFEDA-I experiment allow an evaluation of the performance of the
6. PBL-sensitivity to surface parameterization 197
various coupled models to simulate observed atmospheric quantities. Therefore, an
additional set of model runs was carried out which used the forcings and initializations
obtained from field measurements. Data for initialization of the PBL-model, for the
atmospheric forcings and for comparison of simulations are collected during EFEDA-I, in the
Tomelloso vineyard area in June 1991 (section 2.2).
Rather than expressing model results in terms of deviations from a reference model,
the simulations were compared to a PBL-run using actually measured surface fluxes as lower
boundary condition. The surface fluxes were synthesized from a number of stations in the
Tomelloso area. This dataset was prepared by colleagues from CNRM using the EFEDA-I
database.
This section starts with the selection of a simulation period. As was discussed in
section 4.3 a one-dimensional atmospheric model encounters severe limitations for the
description of the state of an atmospheric column, when horizontal advection importantly
determines the state of that column. Analysis of the data collected during the EFEDA
campaign revealed a strong advection on many days. A very strong sea-wind effect caused a
sharp rotation of the wind direction near Barrax, some 100 km from the Tomelloso location.
Also the radiosonde profiles near Tomelloso showed that advection played an important
role. Obviously, interpretation of PBL-simulations is particularly difficult when the data are
affected by mechanisms not included in the model. A selection of data modified as little as
possible by non-simulated advection effects is therefore useful.
Based upon this selection, the initial profiles and atmospheric forcings are presented.
A control run is carried out (section 6.5.3), which consists of the PBL-model using the
measured surface fluxes. In section 6.5.4 simulations are carried out in which the various
surface model combinations provide the lower boundary conditions. Mutual differences are
expressed relative to the control run, and discussed.
6.5.1 Selection of the simulation period
In order to get a first impression of the influence of advection, it was tested whether
the measured atmospheric profiles obeyed conservation of heat. For this purpose the simple
slab model for the PBL (Driedonks, 1981) was used for a selection of a simulation period. A
sufficient correspondence between observed mixed layer temperature and 9m-predictions
from this simple model using observed values of w 9 0 indicates that the PBL-temperature
profile is well adapted to the heat released from the local surface and entrained from the
atmosphere above. Obviously, a model of this form only gives an indication of the
importance of advection, since subsidence and radiative heating are not included, and the
entrainment closure assumption in eq. 4.90 cannot be expected to be universal.
For all days where radiosonde measurements were available, the slab model was
used to estimate the mixed layer temperature. The mixed layer temperature is rather
insensitive to the specification of the heat entrainment ratio Rh, and therefore serves as a
better indicator than z,-, whose prediction is strongly dependent on the choice for Rh
(Driedonks, 1982b). Surface heat flux was taken from the CNRM database (see below), and zi
was estimated from the soundings as the level of the lowest temperature inversion and
specific humidity jump (see section 2.2.7). Observed values of 6m were simply obtained by
averaging the temperature profile below z = z;. From the entire set, observations taken at
• 198 Sparse canopy parameterizations for meteorological models
day 174 showed the best correspondence with the model, and this day was selected to serve
as test case.
Figure 6.30 shows a comparison between observed and parameterized mixed layer
temperatures for this day. Note that the observed PBL-temperatures are still approximately
2 °C warmer than predicted, which was noticed also by Jacobs (1994). This must be kept in
mind during the interpretation of simulations in the following.
Figure 6.30: Observed (») and simulated ( ) mixed layer temperature (left axis) for DOY 174,1991. Simulations are carried out using the slab model with Rh = 0.2 and the measured surface heat flux ( , right axis)
6.5.2 Initialization and forcing As before, a 36 hour simulation was carried out using At = 3 minutes. The initial PBL-
profile was taken from the radiosonde measurements collected at day 174,4:10 GMT (Figure
6.1). The vertical resolution was also taken similar as before.
The geostrophic wind U was taken from the radiosonde observations. The wind
profile showed considerable vertical gradients over the entire depth of the simulation at all
times, presumably due to thermal winds (baroclinicity). A definition of U as a simple
average in a specified height range was considered to be rather unrepresentative for the
general forcing. Rather, a visual inspection of all available wind profiles was carried out to
estimate the geostrophic wind speed. In each wind profile a level between 1 and 4 km was
selected where the wind speed could be regarded to represent the average wind speed in a
layer above the PBL. The geostrophic wind was linearly interpolated between the times of
the radiosonde measurements. The resulting geostrophic wind decreased gradually from 6
m / s on 23 June, 0:00 GMT to 2 m / s on 25 June, 0:00 GMT.
The observed surface fluxes for the control run with the PBL-model were compiled by
CNRM. Area averaged surface fluxes were obtained by averaging measurements carried out
by various scientific groups in the Tomelloso area, after a carefull quality inspection. A
similar averaging procedure was followed to obtain area averaged temperature, absolute
humidity and wind speed at 2 m above the surface. Due to the poor performance of most
6. PBL-sensitivity to surface parameterization 199"
sensors measuring evaporation, XE was obtained by closing the energy balance using the
area averaged net radiation, soil heat flux and sensible heat flux density. Measurements of
WAUMET were included in all quantities. Figure 6.31 shows the resulting energy balance
components for days 174 and 175. The measured shortwave and longwave incoming
radiation were used as energy forcings for the coupled models.
60O
174 174.5 175 doy
175.5 176
Figure 6.31: Mean energy balance components assembled from measurements at DOY 174 and 175 from various groups operating in the Tomelloso area
The surface momentum flux, u w 0, was not taken from this assembled data base,
since a rather poor numerical resolution (1 significant number) was used. Instead, the
measurements taken by WAUMET using the sonic anemometer at 4.35 m height (Table 2.1)
were used. The total momentum flux was divided over u'w' and v w assuming that the
angle between geostrophic wind and surface stress was 40° at all times. The results of the
one-dimensional simulations reported below are unsensitive to this rotation angle.
6.5.3 Control run A control run of the PBL-model was carried out using the area-averaged surface
fluxes as lower boundary conditions, over the period between day 174, 4:00 GMT and day
175,16:00 GMT.
Figure 6.32 shows the measured and simulated boundary layer height, z;. The
measured values were obtained using the same formulation as in the model, to avoid
methodological differences. The correspondence for the first day is very well. During the
night no observations were available, but the results seem quite reasonable. The sudden
increase and decrease around 4:30 GMT at day 175 is associated with a peak in the surface
momentum stress (figure not shown), which has an unknown origin so far.
200 Sparse canopy parameterizations for meteorological models
4000
3500
3000
2500-
Ê 20001
1500
100O
500
0
/ m
l
J K.J ^ 175 doy
Figure 6.32: Simulated ( ) and observed (•) PBL-height
Figure 6.33: Simulated ( ) and observed (•) mixed layer potential virtual temperature, dv'
Also the mixed layer temperature (Figure 6.33) shows a good correspondence
between data and simulations. Bv' closely corresponds to simulations with the slab model
(Figure 6.30), since a similar surface forcing was used. The entrainment ratio for heat, Rh
(Figure 6.34) shows a large diurnal variation. On the average the value is somewhat smaller
than -0.2, as adopted in the slab model, during both days. The small value for the second
day is well explained by the small temperature gradient in the entrainment layer, which is
entirely a residual from the previous day, without modification by radiative cooling.
I -0.2-
Figure 6.34: Simulated heat entrainment ratio, Rj, Figure 6.35: Simulated ( ) and observed (•) mixed layer specific humidity, q'
The mixed layer specific humidity (Figure 6.35) is slightly overestimated during the
first day. Most likely, the difference between model and data has the same origin as the
difference between modelled and simulated mixed layer temperature, where the data show
a higher value than the model runs. Advection of dry warm air has influenced the radio
sonde data.
The simulated wind profiles show a strong deviation from the observations (Figure
6.36). A clear geostrophic maximum is present at a height of about 2.5 km in the initial
profile, and this air stream is rather well mixed into the PBL at the end of the first day. This
6. PBL-sensitivity to surface parameterization 201
mixing, together with the geostrophic forcing, causes a marked overestimation of the wind
speed in the entire PBL, already a few hours after the simulation starts. The poor vertical
mixing occurring during nighttime caused a significant decrease of the wind speed near the
surface, where friction reduces the wind speed.
5000
4000-
3000-
2000
1000
18 GMT Figure 6.36: Observed (») and simulated ( ) horizontal wind profiles for f = 12 GMT and f = 18 GMT
In general, the PBL-model is quite well capable to simulate the main characteristics of
the observed boundary layer dynamics, apart from the horizontal wind speed profile.
During daytime, the PBL warms up, by heating both from below and from above. A rapid
growth takes place around noon, stopping at about 14:00 GMT. However, the large gap in the
radiosonde measurement sequence around noon leaves the PBL-growth rate unresolved.
Similar measurements carried out in the Belmonte area, some 100 km from Tomelloso, give
rise to suspect the actual growth rate to be somewhat less rapid than suggested by the
model simulation. Michels and Jochum (1995) report a PBL-depth of approximately 2000 m at
14:00 GMT, DOY 174. Moreover, aircraft measurements taken around 13:00 GMT above
Tomelloso at a height of 2500 m show turbulence patterns which are typical for a residual
layer, rather than for a fully developed convective layer. Large scale advection or subsidence
may have reduced the PBL-growth speed. Both observations and simulations indicate the
development of a nocturnal boundary layer from about 18:00 GMT onwards. The height of
this nocturnal PBL changed only slightly as the night proceeded, and was affected mainly by
the momentum flux. The predictions for the second day are more suggestive, since only one
measured PBL-profile is available around noon. An overestimation of the PBL-depth is likely
to be caused by the absence of radiative cooling in the residual layer.
6.5.4 Results of the sensitivity analysis
As before, a difference is made between the surface parameters (surface energy
balance and soil moisture) and PBL-parameters (height, mixed layer state variables and
entrainment fluxes).
202 Sparse canopy parameterizations for meteorological models
• Surface parameters
The various parameterizations of a sparse vineyard canopy on a sandy loam soil
resulted in considerable differences of predicted surface energy balance partitioning. In the
following figures the measured quantities serve as reference.
4a
c?20-
I * s e f-20-
e i -40-
-60
-80
111 1
b c d e g h i j k model variation
I m n
Figure 6.37: Relative differences in predicted daytime net radiation and soil heat flux, compared to the reference run using observed fluxes. Simulations are carried out for a standard vineyard surface using measured initialization and forcings. Model variation codes are as explained in Table 6.2 on page 172
The dominance of the common incoming radiative forcing on the total daytime net
radiation, Q»D, causes the relative differences between the various model variations to be
limited to 5% at most (Figure 6.37). Most models compute a slightly higher net radiation
than measured. An exception is the model case / ('soil VB95'), which predicts a lower net
radiation as a result of a higher surface temperature.
The daytime soil heat flux shows a much larger variability, in particular for the cases
/ = 'soil VB95' and n = 'soil CM88' (Figure 6.37). The large underestimation of the CM88
resistance parameterization (n) was already noticed. Compared to the measured soil heat
fluxes the reference model (a) predicts G values which are ± 20% too high, while the case
'soil VB95' gives too low values. The latter feature is probably caused by an underestimation
of the thermal conductivity, XT, near the surface. For the current soil moisture content, Xj
approached its minimum value of 0.171 W/mK. Verhoef et al. (1995, section 2.4.4) found
values about twice this figure for DOY 174 using the amplitude method. The empirical
weighting of XT over both soil layers in the reference force-restore model (eq. 4.48)
apparently compensated this underestimation. The impact of increasing Xj was not
investigated.
The consequence of the soil heat flux parameterization for the daytime sensible heat
flux is evident from Figure 6.38. A significant increase of H is simulated by the n = 'soil
CM88' case, whereas all other parameterizations confine the differences to approximately
20%. Also the correspondence between measured HD and simulated with the reference
model (a) is good, albeit that the reference model overestimates H by 5%. Quite more
pronounced are the differences in simulated daytime latent heat flux. As expected, the
6. PBL-sensitivity to surface parameterization 203
isothermal big-leaf approach (b = 'big-leaf') results in a significantly larger evaporation than
the reference. This overestimation is not present in the c = 'isotherm' case, where the canopy
evaporation originates from a small part of the grid box only. A very low evaporation rate is
calculated by the case i = 'rc VB95', in which a dependence of rsc on soil moisture and
radiation is adopted. The underestimation of XE is approximately 60%, apparently owing
to an overestimation of the crop resistance. A comparison of modelled values of rf with
EFEDA-II porometry data showed this overestimation to be particularly present at high
radiation levels, thus in cases where the restriction function for co plays a significant role.
However, a field calibration using soil moisture measurements in order to evaluate the rsc-
expression of VB95 was not possible. The cumulative evaporation computed with the
reference model is 20% lower than the observed fluxes. The quality of the measurements
may be disputed, regarding the energy balance closure method used to obtain the data.
BO
'S- 40-
g zo
ll
i g h i i model variation
II
H3
Figure 6.38: As Figure 6.37, for the daytime simulations of sensible and latent heat
The change of the soil moisture volume follows the evaporation pattern closely
(Figure 6.39). By the end of the first simulation day a larger soil water depletion occurs
when surface evaporation is higher. A similar behaviour is present for the second simulation
day. The cases b = 'big-leaf' and m = 'soil rss' both show an enhanced soil moisture depletion
compared to the reference, owing to a larger cumulative evaporation.
• Boundary layer parameters The different predictions in boundary layer height are shown in Figure 6.40. Here,
values of zi at two times on day 174 are shown. A striking feature is that the differences are
particularly present for the mid-day (12 GMT) values of z,. The final PBL-height by the end of
the afternoon (18 GMT) is similar for all model variations. The surface parameterization has a
significant effect on the time at which the PBL shows the fastest growth. The value of z, at
t = 12 GMT roughly marks two different groups of simulations: one group with an early PBL
growth, which are the model variations with relatively high sensible heat flux values (Figure
6.38), and one group of model variations by which rapid PBL-growth is postponed by a few
hours. The case n = 'soil CM88' shows a relatively early start of PBL-growth, governed by the
204 Sparse canopy parameterizations for meteorological models
very high sensible heat flux simulated by this model variation. Both groups eventually reach
approximately the same PBL-height, which is presumably strongly determined by the sharp
inversion at z = 3 km (Figure 6.1).
„ - 1 E E
Î g h i i model variation
12 his
36hrs
k I m n
Figure 6.39: Change of the total soil moisture content after 12 and 36 hours of simulation, for the model variations indicated in Figure 6.37. In this figure the simulated soil moisture depletion is plotted rather than a relative depletion compared to the reference run.
20/
10-
-10
-20
-30-
-50-
-70-
•BT)
I'-
[]
" • LT
U
m i
• L T IT
-
. [ k 1
m 12 GMT
d e g h i j model variation
I m
Figure 6.40: Differences in predicted PBL-height at 12:00 and 18:00 GMT for the model variations shown in Figure 6.37, compared to the reference model
The predicted values of the PBL-height during the next day hardly show the timing
differences demonstrated above. The near-neutral residual temperature profile allows a very
rapid PBL-growth well before noon. The final value of zi reaches approximately 3400 m in
most cases. Again, the final value of z,- is only partially determined by the exact value of the
sensible heat flux, that shows similar differences as on day 174 (figures not shown).
The mixed layer potential virtual temperature is more closely related to the predicted
sensible heat flux from the surface (Figure 6.41). The model variations causing a rapid PBL-
6. PBL-sensitivity to surface parameterization 205
growth result in a higher mixed layer temperature by the end of the day. The boundary
layer temperature simulated by case n = 'soil CM88', in which 50% more sensible heat is
transported towards the PBL during daytime, ends up being 1.1 K warmer than the situation
using observed surface fluxes. The value of z,- in this same case is only 4% higher. Also the
case g = 'aero MH95' , results in a PBL which is approximately 0.5 K warmer, but here the total
daytime surface sensible heat was only 9% higher than for the reference case. The additional
source of heat is provided by an enhanced entrainment of heat (Figure 6.42). The small value
of the average heat entrainment in the reference case (-16 W/m 2 between 6 and 18 GMT)
makes the relative difference for the sensible heat entrainment of case g = 'aero MH95' (± -40
W/m2) rather large.
1.5
1-
2-•g 0.5
* 0 S °
I 1-0.5 S
-1
-1.5
LT 1
y
•
i , L r J IS
1 IÏT tr
. i y
,
j 12 GMT
Figure 6.41: As Figure 6.40, for the mixed layer temperature
e g h i j model variation
I m n
200-
r? 150-
S 1°°i ï E % 50-
1 o-
1 -50-
-100-
T J, Ifl nT Figure 6.42: Relative differences in predicted daytime entrainment fluxes for heat and moisture, compared to the reference model
a b c d e g h i j k l m n model variation
206 Sparse canopy parameterizations for meteorological models
0.8-
jO.6-(U
§ 0.4 I "O E 0.2i
-0.2
-0.4
1 I l m E l « I B
a b c d e g h i j k l m n model variation
12 GMT SU 18GMT
Figure 6.43: As Figure 6.40, for the mixed layer specific humidity
The specific humidity of the mixed layer around sunset (q ) shows a relatively small
variation (Figure 6.43). Obviously, the big-leaf case (b) results in a pronounced increase of
q compared to the reference case, while the case n = 'soil CM88' results in a significant
reduction (> 0.2 g/kg), in spite of the only moderate reduction of XE and increase of the
entrainment water vapour flux.
6.6 Discussion and conclusions
We recall that the investigation of the sensitivity of the PBL to the surface parameteri
zation is carried out by comparing the results of various surface models, coupled to a PBL-
model. The experiments focused on the implication of the choices for physical
parameterizations of separate model components. This was carried out by construction of a
reference model, and replacing its components by alternative parameterizations. The PBL-
sensitivity was expressed in terms of a change of simulated quantities compared to the
reference model. This strategy leads to an investigation of the sensitivity of the PBL to the
selection of surface models, rather than to the selection of surface types or parameter values.
A second aim of the study was to describe Mediterranean sparse canopy conditions. To
include a certain generality, some variations were employed in the initial temperature- and
air humidity profiles, in the vegetation (cover and type), and in soil type.
Despite these restrictions, a large number of degrees of freedom remained. Many
physical processes interact, and the results will often not be transferrable to other conditions.
Also, the range of available land surface models is much larger than covered by this
investigation. Different conclusions could possibly be drawn when alternative
parameterizations would have been included.
First we will summarize the main features of the results shown in this chapter. In a
separate section the practical implications for application of SVAT's in meteorological models
well be discussed. A final section contains considerations with respect to future research.
6. PBL-sensitivity to surface parameterization 207 i
6.6.1 Differences of model parts
We have compared various model components divided into four categories: surface
representation, aerodynamic exchange, soil heat and moisture transfer, and canopy
resistance.
In the surface representation group it is found that the 'big leaf' case gives a much
higher evaporation than any of the other schemes included. The total daytime evaporation
was also considerably higher than the observed latent heat flux. A significant overestimation
of XE by 'big leaf' is to be expected in cases of partial vegetation cover. Adopting a single
surface source results in a surface temperature weighted to relatively high values of the
warm bare soil component. This high surface temperature leads to an overestimation of the
surface specific humidity of the evaporating surface.
Two solutions to this problem were included here. The first, proposed by Noilhan
and Planton (1989), is to discern between a vegetated and a bare surface fraction, identified
by oy. This was embedded in the case 'isotherm'. For a zero soil evaporation, the surface
evaporation formulations in Trig leaf' and 'isotherm' are equal except for and artificial
enhancement of the aerodynamic resistance ra in 'isotherm' (eq. 6.8). When ra is not
insignificant compared to r$c, this leads to a reduction of XED. For the present simulations,
the aerodynamic resistance included a relatively large excess resistance, and this caused the
desired reduction of XE . A more fundamental solution is to solve the energy balance of
each surface fraction separately, as was first proposed by Deardorff (1978). This leads to a
much more realistic lower surface temperature for the vegetation component. This solution
was adopted in the reference case and in the case '3 fracs'. As expected, the A.£D-differences
between a big-leaf model, the surface fraction models and the two-component scheme
vanish for oy —> 1.
Within the boundary layer the overestimation of XE leads to an enhanced
detrainment of moisture. This detrainment is strongly linked to the shape of the specific
humidity profile and to the PBL growth. In the DRY simulations, the 'big leaf' case reduces
PBL growth, giving rise to higher humidity concentrations within the PBL and stronger
humidity gradients at the top of it. This finally leads to an increase of the moisture
detrainment by up to 25% compared to the reference model.
The various parameterizations in the soil heat and water vapour flux group give rise to
considerable differences in simulated soil heat flux and evaporation. The largest effect is the
underestimation of G by the case 'soil CM88'. The soil model in CM88 ignores heat storage in
the upper soil layer, and predicts values of G which are up to 80% lower than the reference
force-restore model. The associated energy surplus is used to heat the air in the atmosphere,
and this has a clear impact on both PBL height and -temperature.
Compared to the reference model, the four-layer diffusion scheme employed in the
case 'soil VB95' predicts a generally higher soil temperature during daytime, which results in
a larger sensible heat and lower soil heat flux. The difference in predicted G compared to
the reference model is 30 - 40%. In the zero-dimensional intercomparison between the
models of D78 and VB95 carried out in chapter 5, the different surface temperature
predictions was explained from a difference in aerodynamic resistance above the surface.
The intercomparison reported in this chapter was executed with similar aerodynamic
• 208 Sparse canopy parameterizations for meteorological models
resistances for both models, and the same difference (albeit somewhat smaller) appears. We
must conclude that the different solutions for the surface temperature are mainly caused by
the difference in soil heat flux parameterization.
The force-restore method, embedded in the reference model, gives an exact solution
of the thermal diffusion equation for a homogeneous soil with a single harmonic surface
forcing (Dickinson, 1988). In the reference model a difference in thermal properties of the
top and the lower soil layer is accounted for by an empirical weighing as depicted in eq.
4.48, but a gradient of these parameters is not included. The four-layer diffusion scheme
allows for both inhomogeneous soil and multiple wave lengths in the surface forcing. The
initial soil moisture profile imposed in the current analysis leads to a pronounced thermal
conductivity gradient in case of sandy loam soil. This feature may explain the different G -
predictions by the cases 'soil VB95' and the reference model. Indeed, the difference between
these two cases is much smaller in case of sandy clay. In that case, the adopted initial soil
moisture profile leads to a similar value of the thermal conductivity for both models (equal
to the minimum value of 0.171 W/mK) throughout the entire soil volume. A comparison of
model simulations with EFEDA data suggest a clear underestimation of 'soil VB95', which is
probably related to a too low value of the soil thermal conductivity.
Also, with respect to evaporation the models in this group show a considerable
variability. This variability is mainly caused by the differences in predicted soil evaporation.
The differences between the included models are not consistent, but depend strongly on the
soil type. For sandy loam, the case 'soil rss' gives a high soil evaporation compared to all
other schemes. Referring to the very dry top soil as encountered during the EFEDA campaign,
the large soil evaporation simulated by 'soil rss' is unlikely. Under conditions of high surface
temperature, the simulated soil evaporation is rather sensitive to the surface relative
humidity, a. The formulation of Philip (1957), used for case 'soil rss', probably gives too high
values near the surface (Kondo et ai, 1992). Furthermore, the soil moisture content in the top
layer from which y and a are derived must be regarded as an average of the co-profile in the
entire layer. Choosing a too deep layer ensures large truncation errors, and this probably
also plays a role in the overestimation of the soil evaporation by case 'soil r$s'. However, it
should be noted that the absolute values of X.E are small.
The picture is entirely different for a sandy clay soil. In this case the reference model
appears to predict a significant soil evaporation, exceeding the canopy evaporation during
daytime. In contrast to the sandy loam soil type, a large difference between the reference
and the case 'soil VB95' now occurs. Both models treat soil evaporation similarly by defining
a surface relative humidity from the top layer soil moisture content, except for the value of a
layer averaging coefficient lc in eq. 4.19. Increasing lc from 1 (reference case) to 1.6 (case 'soil
VB95') results in a clear reduction of the soil evaporation. Given the dry initialization of the
soil, we feel that this reduction results in more realistic simulations. The choice to take
lc = 1.6 applies to an upper soil layer of 7 cm depth, and is compatible with numerical
simulation results carried out by Mahrt and Pan (1984). However, VB95 rightly point at the
empirical nature of the coefficient lc. More on this issue is discussed below.
The different behaviour of soil evaporation simulated by the reference force-restore
model for the two soil types was also noted by Kondo et al. (1992). They simulated a drying
bare soil with both a multi-layer diffusion scheme and a force-restore scheme. The latter
6. PBL-sensitivity to surface parameterization 2 0 9 •
showed a sudden decrease of the surface soil water content after 10 days of simulation. As
they explained, the water transport capacity of the lower soil layer is a steep function of the
soil moisture content. When co drops below a critical value, the upward water transport is
severely limited and the upper layer dries out. In the simulations of the current study, the
sandy loam profile of the relative soil moisture content, co/co^j, is lower than for the sandy
clay, and shows a similar low surface soil moisture content.
The differences found here are considerably higher than reported by Mahfouf and
Noilhan (1991), who compared both a-type and ß-type soil evaporation schemes. Their
comparison was carried out for a silty clay loam soil with a higher initial moisture content
than in this study. The soil thermal and hydraulic properties are extremely strong functions
of the soil moisture content under dry conditions, and this makes a comparison very
sensitive to the specification of the initial soil moisture profile. The current study focussed
on these dry semi-arid conditions, but could be extended by including a somewhat wider
range of moisture and soil type conditions.
The aerodynamic exchange group considers the PBL-sensitivity to the parameterization
of the inside-canopy aerodynamic resistance, ras. The establishment of a proper balance
between the bare soil temperature and the total sensible heat flux is greatly determined by
the parameterization of ras, or its equivalent in terms of the specification of a roughness
length for heat (section 2.4.2). The reference model, using the parameterization of CM88,
gives the highest value of ras and correspondingly the lowest sensible heat flux. The
resistance formulation based on Lagrangian principles, case 'aero MH95', gives a very low ras
and high H, which seems related to the poor knowledge of the true diffusivity profiles right
down near the surface. The semi-empirical BATS-formulation in 'aero D78' is situated in
between these two. The differences were particularly obvious for the rougher and denser
canopies. Based on the EFEDA-measurements, the reference model gives an optimal balance
between surface temperature and sensible heat flux, and is superior to both alternative
parameterizations.
As a consequence of the low value of ras by case 'aero MH95', also the momentum
transfer between the surface and the atmosphere was increased compared to the reference
model, appearing as an increased friction velocity, u». The relatively large mechanical
turbulence contributed much to the growth of the PBL. This effect augmented the difference
in PBL-height between the case 'aero MH95' on one hand, and the other parameterizations on
the other. During nighttime, the momentum transfer in 'aero MH95' is extra enhanced
compared to the other cases owing to the absence of a stability correction between z = z0m
and z = zR. In particular the 'aero MH95' simulations of the tall forest vegetation type reveal
a strong increase of the nighttime PBL-height.
An increased momentum flux between a vineyard canopy and the atmosphere is also
to be expected if the observed roughness length, implemented in all coupled models, is
replaced by the formulation proposed by CM88. This formulation is based on the numerical
experiments of Shaw and Pereira (1982), and gives an apparent overestimation of z0m of
nearly a factor two compared to wind profile measurements (section 2.4.1). The observed
roughness length was rather low: z0m/h was -0.05. Similar values were reported by Sene
(1994) for a vineyard in the same area, and by Garratt (1978) for a sparse forest canopy type.
• 210 Sparse canopy parameterizations for meteorological models
The intercomparisons carried out in the canopy resistance group give rise to a large
range in predicted surface evaporation. In absolute sense the impact of choosing a canopy
resistance model is limited owing to the low value of oy adopted here. For more complete
vegetation covers the differences are more significant.
A common feature to canopy resistance parameterizations is that they need
independent calibration. Data collected during EFEDA-I were used to calibrate the reference
formulation, proposed by CM88, and the photosynthesis-rc models in 'rc C 0 2 ' and 'rc big
C0 2 ' . The value of rf in 'rc fix' was obtained from the reference model, and thus indirectly
also calibrated with the same dataset. Only the parameterization in 'r VB95' was not
calibrated using the collected observations, and these expressions resulted in a too low
evaporation rate compared to the observations and the reference model simulations.
However, a significant difference between model variations is also caused by
differences in included environmental responses in the various models. In the reference case
rf only depends on incoming shortwave radiation. Comparing the predicted daytime
evaporation to the observed quantities (section 6.5) reveals an underestimation of
approximately 20%. But, as noticed before, the quality of the XE-data leaves the possibility
that measured evaporation rates are too high. The correspondence between the reference
model and the observations taken at the WAUMET site is better (section 5.2).
The daytime evaporation predicted by the photosynthesis-rc model proposed by
Jacobs (1994) and Jacobs et al. (1995), present in the case h = 'rc C0 2 ' , is significantly larger
than the reference model, especially for the cool and moist MLS initialization. The model was
calibrated under conditions corresponding to the DRY profile, and a rather strong response
to ambient humidity deficit is included. This humidity response causes a strong reduction of
rsc under MLS conditions and gives rise to higher values of XE . The humidity response is so
strong, that the overestimating effect of adopting a single surface temperature as in the case
'big leaf' is greatly compensated by the associated rise in ambient humidity deficit (case
'r big C02 ' ) . Furthermore, the case 'rc C0 2 ' simulates an evaporation peak at about 10 GMT.
This causes a considerable increase in the total daytime moisture flux at the top of the PBL.
Before noon the PBL is still low, and the moisture accumulation below the inversion gives a
strong humidity gradient across the PBL top.
The average ratio of the entrainment virtual heat flux to the surface flux, Rh, is
approximately 0.1 for the EFEDA simulations of DOY 174. The simulations using artificial
initial profiles show a similar figure. The value of Rh found here is not necessarily a physical
quantity, as it is derived from the numerical simulation of a turbulent diffusion process,
according to Troen and Mahrt (1986) and Holtslag and Moeng (1991). Since Rh follows from
the development of the turbulent fluxes in the past, and also enters the formulation of the
turbulent diffusivity, a negative feedback in the model may result in a reduction of Rh. Also,
the present PBL-model does not include the contribution of wind shear above the PBL to the
growth of the turbulent layer. However, the dependence of Kh on Rh is not very strong, and
the model also succeeds in a reasonable simulation of observed PBL-temperatures under
conditions of poor advection. This indicates that the estimates of Rh contain some realism,
and allow an intercomparison with other studies. Driedonks (1981) and Tennekes (1973)
suggest Rh = 0.2 for most cases. Betts and Ball (1994) found Rh = 0.44 for the FIFE
radiosoundings. In this dataset, larger values (0.55) where found from an analysis of the 0„-
6. PBL-sensitivity to surface parameterization 2 1 1 •
budget of the PBL, while lower values (0.32) resulted from an analysis of observed 8j,-jumps
and PBL-growth. As they comment, the former method is rather sensitive to advection, while
the latter method suffers from the exclusion of the influence of subsidence on PBL-growth.
However, the sensitivity analysis of Driedonks (1982b) clearly demonstrates a limited
sensitivity of mixed layer temperature to the value of Rh, and this might partially explain the
high value found by Betts and Ball (1994), using the 80-budget. Also Culf (1992) found
Rh = 0.5 by comparing PBL height observations with the slab model of Tennekes (1973) using
data collected over the Sahel. He argues that again advection might have played an
unknown role in his data. The average value of 0.1 found here seems rather low compared
to these studies. A final statement about the significance of this result is hard to give, since
simulations and data on only a single day have been used to obtain the value of Rh. A more
careful analysis of the other soundings and an averaging over the entire period should be
carried out to evaluate the value of Rh.
The initial temperature profile of DOY 174 clearly showed the presence of a residual
layer reaching a height of approximately 3 km. A strong temperature inversion at this height
prevented the PBL from a significant growth beyond this level for the given surface heat flux.
This strongly developed residual layer yielded a limited heat entrainment ratio in the
simulations. The entrainment ratio for moisture is much larger, but shows a great variability
due to the small surface flux of moisture.
6.6.2 Practical considerations for SVAT's
An important question arising from the comparison study is what practical
consequences can be extracted from it.
From the surface representation group we concluded that a sparse canopy must be
described by use of at least two separate components, a vegetation and a bare soil
component. The surface energy balance is quite well reproduced by either the reference two-
component model or the case '3 fracs' (section 4.2.1), which both allow a separate
temperature for the bare soil and the vegetation component of the surface. Soil heat flux is
still too high for both these model variations, compared to area-averaged measurements
from the CNRM database.
The soil heat and water vapour flux group is less conclusive. The overestimation of G
by the reference model is accompanied by a clear underestimation in the case 'soil VB95', but
which of them should be preferred is not clear. As outlined by Dickinson (1988), the force-
restore method is efficient but shows shortcomings in case of inhomogeneous soils and
irregular surface forcing. Based on these physical aspects, a multilayer diffusion scheme to
simulate soil heat fluxes should be preferred in semi-arid areas, where strong soil moisture
gradients are very common. The four-layer scheme present in the latest ECMWF surface
model (Viterbo and Beljaars, 1995) probably provides a good optimum between numerical
efficiency and physical accuracy. Warrilow et al. (1986) pointed out that the choice of four
soil layers with an exponentially increasing layer depth ensures a proper coupling between
the diurnal and the seasonal variations. However, the parameterization of the soil heat flux
as proposed by Viterbo and Beljaars (1995) may be improved by allowing a range of
effective conductivity values, A (section 4.1.3).
For soil evaporation it is more difficult to come to a conclusion from a shortrange
• 212 Sparse canopy parameterizations for meteorological models
intercomparison as employed here. The schemes included show a wide range of surface
evaporation rates. For the sandy loam soil, as encountered during EFEDA, the reference
model or the soil resistance model (case 'soil rss') yield total evaporation rates close to the
observed values. However, the observations are probably too high, and the correspondence
between the two model types is far from ideal for an other soil, i.e. sandy clay. The soil
surface relative humidity as described by eq. 4.19 using lc = 1.6 reduces the soil evaporation
to nearly zero, as would be expected from the dry top soil layer encountered during EFEDA.
The adjustment of the expression for a using this coefficient is yet rather empirical, as
suggested by VB95, and needs further analysis. The albedo-observations (section 3.3) suggest
some diurnal variation of the soil moisture content in the top soil layer, being highest
around sunrise. Some evaporation should be expected at these times, but none of the models
simulated these details. The skill of the models highly depends on the accuracy of the initial
soil moisture profile, which may have been too poor, particularly for the soil moisture
content in the very top soil layer.
The aerodynamic exchange from the underlying bare soil to the free atmosphere is a
particularly relevant parameter for sparse canopy, where a large portion of the sensible heat
originates from the bare soil component. The aerodynamic transfer has a clear impact on the
surface temperature, which in turn affects radiative, physiological and aerodynamic
processes. From this study we found that the parameterization of CM88 gives optimal results
for the EFEDA vineyard. A disadvantage in CM88 is the need for information about the
canopy height, which is often not available in global applications. The concept of a fixed
excess resistance, or roughness length for heat, is simpler to apply. However, observations
of the soil temperature show a clear diurnal pattern of this excess resistance. They also show
that for the present surface type the ratio of z0m and zoh should be chosen significantly
higher than 10, as employed by for instance VB95, or even 20, as proposed by Braud et al.
(1993).
The canopy resistance models compared in the current study have only a minor effect
on the total surface energy balance, owing to the low degree of vegetation cover. The
photosynthesis model in case 'rc C0 2 ' has a very strong humidity response, but, as
discussed in section 3.4, does not contain a dependence on soil moisture content. The
parameterization in 'rc VB95', on the other hand, includes a soil moisture effect which results
in a relatively high crop resistance. Again, the choice for the optimal model for the canopy
resistance is not univocally obvious from the present study. The physical origin of the
photosynthesis model, and its skill to describe field data rather well, makes it a very
attractive alternative to the traditional statistical models. However, attention must be paid to
the response of rf to soil moisture, which for long term simulations is probably more
important for the total crop evaporation than a response to air humidity (Monteith, personal
comm.).
6.6.3 Guidance for future research
From this study it is clear that many physical viewpoints have been proposed in
order to assess the lower boundary condition for atmospheric models. It is also clear that
different models give rather different predictions. Until now, no general consensus exists
about which SVAT provides the 'best' surface flux predictions for global applications.
6. PBL-sensitivity to surface parameterization 2 1 3 •
In that context a very important research program currently running is the Program for Intercomparison of Land-surface Parameterization Schemes (PILPS; Henderson-Sellers et al, 1993,1995). This program aims to 'improve the understanding of current and future land-surface parameterization schemes used to represent regional to continental scale, by documentation of current models, acquisition of appropriate data sets for model intercomparison, identification of model inadequacies and propose solutions to these' (Henderson-Sellers and Brown, 1992). The PILPS program is scheduled to last 7 years, and is separated into various phases: (0) model documentation, (1) stand-alone tests with synthetic forcings, (2) stand-alone tests with observed data, (3) coupled intercomparisons with a selected 3-D model, and (4) coupled intercomparison with a range of 3-D models. The research program is unique in its completeness of both existing SVAT schemes and considered topics, and greatly will contribute to the quantification of surface model variability.
The required quality of a SVAT depends on the application foreseen. For large scale applications in GCM's or NWP models the SVAT must cover a great range of surface types and time scales. An important feature is a realistic description of moisture transport on a diurnal and seasonal (annual) timescale, and the parameterization of soil evaporation is a major issue for semi-arid conditions. Similarly, the quality of the global fields of surface characteristics (albedo, roughness, soil type, vegetation cover) determines the skill of the SVAT's to a large extent, and this needs attention as well.
2 1 4 Sparse canopy parameterizations for meteorological models
Appendix I: List of symbols and acronymns
acronymns BATS Biosphere-Atmosphere Transfer Scheme
CM88 Choudhury and Monteith (1988) CNRM Centre National de Récherches Météorologiques, Toulouse
COP Copenhagen University D78 Deardorff (1978) DOY Day Of Year
ECHTVAL European project on Climatic and Hydrological Interactions between the Vegetation, the Atmosphere and the Land Surface
ECMWF European Centre for Medium-range Weather Forecasting EFEDA ECHIVAL Field Experiment in Desertification-threatened Area EPOCH European Programme on Climate and Natural Hazards
FIFE First ISLSCP Field Experiment GCM General Circulation Model GMT Greenwich Mean Time
HAPEX Hydrological Atmospheric Pilot Experiment HIRLAM High Resolution Limited Area Model
ISLSCP First International Satellite Land Surface Climatology Project KNMI Royal Netherlands Meteorological Institute
LNF Localized Near-Field theory MH95 McNaughton and Van den Hurk (1995)
MLS Mid-Latitude Summer (initial PBL-profile) NP89 Noilhan and Planton (1989) NWP Numerical Weather Prediction PAR Photosynthetic Active Radiation PBL Planetary Boundary Layer
PILPS Project for Intercomparison of Land surface Parameterization Schemes PM Penman-Monteith (equation) SIB S imple B iosphere m o d e l
SL Surface Layer
SVAT Soi l -Vegeta t ion-Atmosphere Transfer
SW85 Shu t t l ewor th a n d Wallace (1985)
TDR T ime Doma i n Reflectometry
VB95 Vi terbo a n d Beljaars (1995)
vu Free University of Amsterdam WAUHBH Wageningen Agricultural University, Dept. of Hydrology WAUMET Wageningen Agricultural University, Dept. of Meteorology
WMO World Meteorological Organization WSC W i n a n d S tar ing Cen t re
• Symbols A available energy (W/m7)
4.T A Ac
Ad
Am
allwave radiation (W/m ) available energy for canopy (W/m ) drip area (m2) average leaf area single leaf (m ) asymptotic value of An (kg/m2s)
l a x maximum value of Am ( k g /ms )
photosynthetic rate (kg/m2s) areal surface of soil heat flux plate (m2) available energy for soil (W/m2) amplitude temperature wave (K)
Ax, Amx spectra functions a surface albedo; coefficient in PBL-model;
coefficient for longwave emittance (W/m2K4)
Symbols and acronymns 215
flco canopy albedo for LAI —> °° 80 albedo at noon H^l^î coefficients in rs
c model of VB95 ac canopy albedo a calibration coefficient for co a^ . albedo for canopy with horizontal leaves flj effective area for Tsur (m
2) as bare soil albedo a h albedo for canopy with spherically
distributed leaves B-1 l /K ln Z o m / z 0 „ Bx, Bwx spectra functions b characteristic plant width (m); Clapp and
Homberger coefficient; coefficient in PBL-model; coefficient for longwave emittance
bfrbj coefficients in PBL-model bD coefficient for humidity dependence of gs
(g/kg)"1
C soil heat content (J/m2) C scalar concentration (kg/m3); cloud cover (-) Ci,C2,C2ref coefficients for soil moisture transport
in force-restore scheme Ca specific heat air (J/kgK) Cb average concentration near leaf (kg/m3) Cc average concentration within canopy layer
(kg/m3); coefficient in SW85 Cd leaf drag coefficient Cr far-field concentration (kg/m3) CH transfer coefficient for heat and scalars Ch specific heat of soil (J/kgK) C; internal C02-concentration (kg/m3) Cj fraction of surface covered with skin
reservoir CM bulk drag coefficient for momentum Cn near-field concentration (kg/m3) C0 specific heat organic material (J/kgK);
relative oxygen concentration (%) CR drag coefficient roughness element; reference
concentration (kg/m3) C s substrate drag coeficient Cs specific heat of mineral (J/kgK);
concentration at ground surface (kg/m3); external C02-concentration (kg/m3); coefficient in SW85
CT temperature structure parameter (K2m"2'3) Cv average far-field concentration (kg/m3) Cw specific heat water (J/kgK); spectra function c coefficient for d; specific scalar concentration
(kg/kg) cQlCyC2 coefficients in description for aw and T;
cd coefficient for d c coefficient for g ct internal specific concentration (kg/kg) cm regression coefficient for md
c specific heat for dry air at constant pressure (J/kgK)
c$ external specific concentration (kg/kg) cm hydraulic capacity (m"1) cxV cx2' csx coefficient for similarity method (x = T,
c^ correction factor for A, D characteristic plant spacing (m); vapour
pressure deficit at reference height (Pa); molecular diffusion coefficient (m2 /s)
D0 canopy water vapour deficit (Pa) Da humidity deficit at reference height (kg/kg) Dmax reference humidity deficit for humidity
response in An-gs model (kg/kg) Dp plant density (m"2) Dr calibration coefficient in humidity response
o f S s ( g / kg ) Ds ambient humidity deficit (kg/kg) Dv molecular diffusivity for water vapour
(m2 /s) d displacement height (m) d3/d2 depth of soil layer i (m) d31 crosstalk coefficient d33 attenuation coefficient d„ diameter of soil heat flux plate (m) ds beam path length (m) E evaporation rate (kg/m2s) Ec canopy evaporation (kg/m2s) E?0' potential canopy evaporation (kg/m2s) E daytime average of surface evaporation
(kg/m2s) E; leaf evaporation rate (kg/m2s); evaporation
from skin reservoir (kg/m2s) Emax maximum evaporation rate (kg/m2s) Es soil evaporation (kg/m2s) Et leaf transpiration (kg/m2s) Ej daytime average moisture entrainment
(kg/m2s) e water vapour pressure (Pa) £Q water vapour pressure in canopy air (Pa) ea water vapour pressure at reference level (Pa) e , saturated water vapour pressure (Pa) F moisture flux in soil (kg/m2s) Fc canopy flux density profile (kg/m2s) FCQ2 C02-flux density (kg/m2s) Fh average canopy flux density (kg/m2s) F$ ground flux density (kg/m s) F, total flux density (kg/m2s) Fx flux density of x (kg/m2s) ƒ Coriolis parameter (s"1); normalized
frequency (s-1); humidity function of Ci/Cs
f0 ratio of Ct/Cs at Ds = 0 fd fraction of diffuse radiation fs fraction of sunlit leaves G soil heat flux density (W/m 2) G0 soil heat flux density at surface in CM88
(W/m2) G daytime average soil heat flux density
(W/m2) Ci t, G, b soil heat flux density at top and bottom of
layer i (W/m2) g gravity acceleration (m/s2); function for a$
g0 regression coefficient for g gj calibration coefficient in crop resistance
according to CM88 (m/s / W/m 2 ) gb dimensionless concentration in PBL-model
216 Sparse canopy parameterizations for meteorological models
gc crop conductance (m/s) g° g c a t D s = 0 (m / s ) gcut cuticular conductance (m/s) gD humidity response of rs
c in NP89 gm mesophyll conductance (m/s) Smax maximum crop conductance (m/s) gs stomatal conductance (m/s) Ss C02 stomatal conductance for C02-exchange
(m/s)
S s ^ m a x i m u m 2 s ( m / S ) & 2S at Ds = 0 (m/s) gt dimensionless concentration in PBL-model H sensible heat flux density (W/m2) H canopy sensible heat flux (W/m2) H daytime average sensible heat flux density
(W/m2) Hs soil sensible heat flux (W/m2) Hf daytime average heat entrainment (W/m2) h canopy height (m) J interception (kg/m2s); integrated surface
buoyancy flux (K m); beam intensity; absorbed PAR (W/m2)
IQ reference beam intensity Is infiltration ( k g /ms ) ƒ integrated surface latent heat flux (g/kg m) K, Kx eddy-diffusivity (m2/s) (x = h for heat, m for
momentum, e for water vapour, c or s for scalars)
K incoming, reflected shortwave radiation (W/m2)
Kb bottom-up diffusivity (m2/s) Kc incoming, reflected shortwave radiation for
canopy (W/m2) Kdir diffuse radiation (W/m2) Ke extraterrestrial shortwave radiation (W/m ) Krfrf coefficient in rf model (W/m2) Ks incoming, reflected shortwave radiation for
soil (W/m2) KT isothermal water vapour diffusivity ( m / s ) Kt top-down diffusivity ( m / s ) k soil thermal diffusivity (m2/s)
K K
extinction coefficient for black leaves absorption coefficient for gas i near-field kernel function
k precipitation coefficient kr extinction coefficient k water vapour absorbtion coefficient L incoming/outgoing longwave radiation
(W/m2) Lg_14 incoming longwave in 8-14 (jm band
4.Î (W/m z)
Lc incoming/outgoing longwave radiation for canopy (W/m2)
Ls incoming/outgoing longwave radiation for soil (W/m2)
Lu cup-anemometer response length (m) Lv Monin-Obukhov length (m) LA Leaf Area (m2) LAD Leaf Area Density (m2 /m3) LAI Leaf Area Index (m2 /m2)
LAI, LAI/af
I tube length (m) lc layer-averaging coefficient for a lw characteristic leaf dimension (m) M^ longwave emittance (W/m2) ma molecular weight of dry air md assymetry function for a$
md0 regression coefficient for md
m0 molecular weight of oxygen mv molecular weight of water N number of leaves Nu Nusselt number (ratio lm/S) n eddy-diffusivity extinction coefficient;
number of samples; frequency (s"1) n0 cut-off frequency (s"1) ns sampling frequency (s"1) P total precipitation rate ( k g / m s ) Pr Prandtl number (ratio dynamic viscosity and
thermal diffusivity of air) Ps surface precipitation rate (kg/m2s) p air pressure (Pa); parameter in ß-
distribution; sensor averaging length (m) p0 standard air pressure (Pa) p calibration coefficient for a> Qw reference value in dimensionless response
function Q, net radiation (W/m2) Q» daytime average net radiation (W/m ) Q» c canopy net radiation (W/m2) Q. s soil net radiation (W/m2) q specific humidity (kg/kg); parameter in ß-
distribution q* characteristic humidity scale in convective
PBL (kg/kg) q0 within canopy specific humidity (kg/kg) q00 humidity profile extrapolated to z = 0
(kg/kg) qa reference specific humidity (kg/kg) qc canopy surface specific humidity (kg/kg) qm average q in PBL (kg/kg) qmm average q in PBL just before sunrise (kg/kg) qs soil surface specific humidity (kg/kg) q„t saturated specific humidity (kg/kg)
average PBL specific humidity at time t (kg/kg)
R molar gas constant (m 2 / s 2 K) Rj,R2,.. root extraction fraction Ra coefficient in SW85 Rc coefficient in SW85 Rd dark respiration ( k g /ms ) Rh heat entrainment ratio R moisture entrainment ratio Rs coefficient in SW85; scalar entrainment ra Rv gas constant for water vapour ( m / s K) 9? dimensionless resistance Re Reynolds number Rec critical Reynolds number Ric critical Richardson number r reflection coefficient; mixing ratio r2 2 space coordinate (m)
Symbols and acronymns 217 i
ra aerodynamic resistance (s/m) r" aerodynamic resistance for scalars between
z0m and ZR ( s / m ) ra excess resistance (s/m) ra
c bulk boimdary layer resistance (s/m) rfl
s aerodynamic resistance in two-layer model between soil surface and within canopy node (s/m)
rb leaf boundary resistance (s/m) rt lower soil resistance in CM88 (s/m) rn near-field resistance (s/m) rs
c canopy or crop (stomatal) resistance (s/m) rs
s soil resistance for evaporation (s/m) rsf leaf stomatal resistance (s/m) rs,min> rs,max coefficients in rf model
'( tube radius (m)
ru upper soil resistance in CM88 (s/m) rx plant radius (m) rh porometer relative humidity S source strength (kg/m3s) s dq^f/dT; sensor separation (m) SM root extraction (kg/m s) Sh canopy source strength (kg/m3s) S (co-)spectral distribution function T0 temperature in canopy layer (K) TlrT2,~ soil temperature in layer i (K); reference
temperatures in QJ0-response function (°C) Ta reference air temperature (K); analog-to-
digital transfer function Tb sensor body temperature (K) Tc canopy temperature (K) Td first-order digital high-pass filter transfer
function T; Lagrangian time scale (s); leaf temperature
(K) Tn data-acquisition net transfer function T sensor line averaging transfer function Tr sensor dynamic response transfer function Ts soil temperature (K) T$k skin layer temperature (K) Tsm sonic temperature (K) Tsur effective surface temperature (K) T( tube damping transfer function Tu horizontal averaging vector transfer function Tv virtual temperature (K); low-pass filter
transfer function Tw wet-bulb temperature (K); vertical averaging
vector transfer function T (co-)spectral transfer function for x'y' t time (s) u horizontal wind speed (m/s) u. friction velocity (m/s) u0 within canopy wind speed (m/s) ua reference wind speed (m/s) u geostrophic wind component (m/s) ut tube air speed (m/s) V volume of plant (m ); Voltage (V) Vc speed of sound (m/s) v horizontal wind speed (m/s) v geostrophic wind component (m/s)
WMAX coefficient for wmàx (mm) w vertical wind speed (m/s) w, convective velocity scale (m/s) wdew amount of intercepted water (mm or kg/m 2) tfmax maximum amount of intercepted water
(mm) ws characteristic velocity scale in PBL-model
(m/s) X CdLAI x constituent xa volume fraction of air xl resistance coefficient in VB95 (m/s); sensor
longwave gain (V per W/m 2 ) x0 volume fraction of organic material xs volume fraction of soil; resistance coefficient
in VB95 (m/s); shortwave gain (V per W/m 2 ) xw volume fraction of water zR reference height for canopy models, or
lowest model level for PBL-model (m) z height (m) z0m roughness length for momentum (m) zoh roughness length for heat and salars (m) z0' roughness length of soil (m) zX,wz2,w s c"l l a y e r depth for water transport (m) zj boundary layer height (at time t) (m) zs particle release height (m)
• Greek letters a surface relative humidity; horizontal angle ad time coefficient in first-order filter a ; leaf absorbtivity OL shape factor for soil heat flux plates au wind speed extinction coefficient ß solar elevation; rotation angle PR CR/CS ß r radiation extinction coefficient ßs sheltering factor for rh
T compensation concentration (kg/m3) rh coefficient for non-evaporating parts in D78 y psychrometer constant (Pa/K) yb bottom-up countergradient correction (m"1) yH hydraulic conductivity (m/s) yh u(h)/u. y humidity gradient above PBL (m"1) ys scalar countergradient correction (m*1) y s a t saturated hydraulic conductivity (m/s) yt top-down countergradient correction (nT1)
y a temperature gradient above PBL (K/m) V
5 step function; thickness of leaf boundary layer (m)
A de$at/dT A; optical depth e rnv/ma; emissivity e0 maximum quantum use efficiency (kg/J PAR) en longwave emissivity of air Eb sensor body emissivity ec,es canopy or surface longwave emissivity e, initial quantum use efficiency (kg/J PAR) tj sensor setting for E
218 Sparse canopy parameterizations for meteorological models
Ç zenith angle; spectra function T| roughness density 0 potential temperature (K); vertical wind
angle (rad) 8, temperature scale (K) 6,ML mixed layer temperature scale (K)
A
K \ n V
\
P(a) P'
within canopy potential temperature (K) reference potential temperature (K) canopy surface temperature (K) average PBL-temperature (K) soil surface potential temperature (K); temperature excess of convective thermal (K) potential skin layer temperature (K) average surface potential temperature (K) average PBL potential virtual temperature at time t (K)
m average PBL potential virtual temperature just before sunrise (K) temperature profile extrapolated to z = 0 (K)
skin conductivity ( W / m K ) latent heat of water vapour (J/kg); wave length (m) Karman constant (0.4) hydraulic diffusivity (m2/s) soil thermal conductivity ( m / s ) thermal conductivity of air (W/mK) condictivity of soil heat flux plate (W/mK) cos Ç kinematic molar diffusivity ( m / s ) fraction of potential canopy evaporation; spectra function sensitivity parameter for x density of dry air (kg/m3) soil bulk density (kg/m3)
Pi Po Ps Pv Pw Px
a °f ax T X
reflectance of leaves density of dry matter (kg/m3) density of soil (kg/m3) water vapour density (kg/m ) density of liquid water (kg/m3) scalar concentration (kg/m3) Stefan-Bolzmann coefficient fractional vegetation cover standard deviation of x throughfall (kg/m2s) momentum flux density (kg/m s2); tortuosity parameter; return-to-isotropy time scale (s)
Xj diurnal time scale (24 hrs) T2 annual time scale (365.25 days) xc sensor time constant (s) xrf digital filter time scale (s) X; leaf transmittance <|> dimensionless source profile; azimuth <|>ft integrated stability correction for heat and
scalars (|>m integrated stability correction for momentum (p effectiveness weighting for rb xVh stability correction; profile influence function y soil matric potential (m) y , ^ saturated soil matric potential (m) coc critical soil moisture content for a (m3 /m3) a); soil moisture content in layer i (m3 /m3) a* implicit form of co, (m3 /m3) (s>„„„ equilibrium soil moisture content (m /m 3) ù wilting point soil moisture content (m / m ) ùf field capacity soil moisture content (m 3 /m ) Q)sfl( saturated soil moisture content (m / n r )
Symbols and acronymns 219 i
Appendix II: Instrumental aspects and data processing
Sensing the atmosphere or the soil is almost inevitably associated with introduction of errors. The errors can be associated with flow distortion, sensing in a limited frequency or spatial domain, sensor calibration affected by environmental conditions and some other factors. The corrections applied to the eddy-correlation measurements, soil heat flux, surface temperature and radiation are discussed in this section.
Low-pass filtering (detrending)
The covariances measured by the eddy-correlation technique are often affected by trends in the signal which don't have a turbulent origin. Diurnal variations of air temperature and humidity, wind velocity changes due to a change of the wind direction, or the influence of sudden cloud cover changes on the average air temperature are examples of non-turbulent contributions to the eddy-correlation covariances. The same applies to fast-response variance measurements, used for instance to determine fluxes from the variance method (section 2.2.4). Therefore, some kind of detrending must be applied to filter out the low-frequency part of the measured spectrum of the constituents of interest. The frequency below which fluctuations have to be removed (the high-pass cut-off frequency) strongly depends on the mechanism causing the non-turbulent contribution to the quantity fluctuations. Different opinions are circulating about the preferred choice of the cut-off frequency and the detrending algorithm. However, these choices sometimes play a non-trivial role in the determination of the final detrended covariances from raw time series.
Van den Hurk (1995) explored the effect of various detrending algorithms on the computed variances and covariances of simultaneously measured series of the horizontal and vertical wind speed, u and w, respectively. He used a dataset collected during the EFEDA-II eddy-correlation intercomparison. Various artificial trends were added to an original trendless time series. The variances and covariances were computed using various averaging algorithms currently applied by different experimentalists. The artificial trends were selected as to cover a range of likely trends occurring in the real world.
The results often showed a large impact of the choice of the detrending algorithm, depending on the combination of added artificial trend and algorithm employed. The differences were
particularly significant for corrections on o"H2, and less significant for u w and W'T'.
This section discusses various detrending algorithms, and describes the algorithms employed during the EFEDA-I and EFEDA-II measuring campaigns.
• Description of detrending methods The linear detrend defines the mean of a constituent as the linear regression of the variable
against time. The fluctuation part of the quantity x is equal to the value of x minus the value of the regression line at the same time. The time scale of the fluctuations that must be removed is proportional to the length of the averaging interval over which the regression is computed. A linearly detrended variance of x is assessed by subtracting the signal-time covariance from the raw variance:
/ -\
c.det • i t = a. 2 -Y.xt-l'Lx-'Lt (IM)
where n is the number of samples, and the subscript del indicates detrended variance. The first-order digital filter approaches a running mean by defining the average of x as
xi = aixi_x*(l-ai)xi (H.2)
» 220 Sparse canopy parameterizations for meteorological models
in which aä is given by exp(-l/(Td ns)), and ld is a time constant. The fluctuating part of the quantity x is obtained by subtracting the mean from the total quantity, which yields from eq. II.2
..' .. -r .. ,.. .. x .. J (II.3) xi~xi = ad(xi-xi-d+adxi-\
i is the timescale of the fluctuations which must be removed from the signal. In operational systems as the Hydra (Shuttleworth et ah, 1988) i = 200 s. However, longer time scales must be included to
describe the low-frequency contributions to u u , originating from eddies of the scale of the boundary layer height (Panofsky et ah, 1977). Some experimentalists use x = 600 s. Moore (1986) derived correction factors to account for the effect of high pass-filtering on the (undesired) removal of turbulent fluctuations. These correction factors are discussed below.
Simpler approaches describe the trend in a signal by computing separate means for short intervals, shorter than the averaging time of 30 minutes. Fluctuations of the quantity x in a specific sub-interval are then defined as the deviation from the mean in that sub-interval. The (co)variance applicable to the entire interval is given by the arithmetic average of the covariances obtained in the various sub-intervals.
The centred running mean with averaging time t computes the average of constituent x at time t from an interval extending from t - x/2 to t + 1 / 2 . A circular buffer containg all data in this interval must be retained and updated for each new time step.
A very time-consuming but well defined filtering technique uses a Fourier transformation to transform samples within a specified averaging interval to the frequency space. Specified transfer functions are used to remove undesired frequencies, and afterwards an inverse Fourier transform converts the series back into a time series. This method must be applied for each (co)variance separately. The Fourier method was not included in the comparison study of Van den Hurk (1995).
Which averaging method is best depends on the nature of the trend in the average signals. Diurnal trends can be removed effectively with both the linear and 1st order detrend. Sudden signal changes due to, for instance, cloud overpass are followed better by the recursive filter, although the filtered signal lags behind. By application of a higher order filter (Krikke, 1994b) or the running mean removal, this lagging is avoided. Application of higher order filters introduces concern about the high degree of non-natural information in the 'cleaned' signal. Linear detrends are favourable when the signal shows large variations with only a small average trend. Recursive filtering will remove too much of the true variation in that case, especially when the time constant for the recursive filtering is chosen too small.
• Detrending methods employed During EFEDA-I all fast-response signals were linearly detrended over an half-hour interval. The
slow-response signals were first linearly detrended within 10 minute intervals. These 10 minute averages were arithmetically averaged to 30 minute intervals.
The eddy-correlation software used during EFEDA-II originally executed a digital 1st order filter. This algorithm was later replaced by a linear detrend over a fixed 30 minute interval. The slow-response measurements were not detrended at all.
Eddy-correlation corrections
Eddy correlation corrections can be divided into three categories. Rotation corrections consider tilted streamlines due to terrain or mast tilt and flow distortion by the sensor. Frequency response corrections assess the problem of the limited frequency range actually being sensed, which is generally smaller than the inertial subrange. The third group of corrections consider various aspects of the fast response sensing system: vector averaging by cup anemometers, Webb-correction, virtual temperature and light-absorption by non-relevant gases.
• Rotation corrections Ideally the wind flows parallel to the Earth's surface from a steady direction. Moreover, the
transport of momentum in the lateral direction (v w ) can be ignored. Deviations from this ideal behaviour are caused by tilted sensors, sloping terrain in upwind direction, and flow distortion by the array. Wyngaard (1988) points out that the rotation corrections usually carried out are not sufficient to account for flow distortion errors. It is not difficult to show that a flow distortion caused by a sensor can actually add motion to the free wind stream, whereas rotation only redistributes the motions over the three components. Wyngaard (1988) defines an attenuation or amplification
Instrumental aspects and data processing 221 •
coefficient of wind in the vertical direction (^33), and a crosstalk coefficient of horizontal wind
components into the vertical direction {d31). The undisturbed covariance wx can be computed from
wmxm / «>X = l+d. 33 T "31 ux wx
(II.4)
where the subscript m refers to the measured vertical flux density. Both coefficients must be specified using an undisturbed free wind stream. For a vertically symmetric array d33 is rather insignificant compared to d31. Since carefull attention is paid to twisting the sonic arrays into the mean wind, vertical symmetry of the array, and data selection as function of relative wind direction, the rotations discussed next are considered to serve as a proper correction to flow distortion as well.
The coordinate rotation applied here is the one proposed by McMillen (1988). The algorithm consists of 3 rotations:
• a horizontal rotation to align the u-component with the mean horizontal wind U, thus rotating
v to zero
• a vertical rotation to align the mean wind perpendicular to the streamline, thus forcing w to be zero
• a rotation along the «-axis to force the lateral momentum flux v w to zero. This rotation defines the vertical flux densities normal to the streamline rather than to the geopotential, which is of importance when the streamline inclines with respect to the local surface due to upwind terrain slopes. This rotation must be applied with care, since it is not always well defined, particularly under low wind speed conditions.
The rotation algorithm consists of a set of matrix multiplications. The first two rotations can be
solved explicitly. Let a be the angle between ïï and U, and 8 be the vertical tilt, defined by
w 6 = arctan
\ju + v +1
The rotation matrix for the first two rotation, Mj 2, now becomes
cosctcosG sinasinG sin0
1,2 -sinG cosa 0
-cosasinG -sinasinG cosG
(H.5)
This matrix can be applied to both the mean wind values and the fluctuating parts:
= M-1,2
"2
/ v2
1 w2
• A * u
M v'
w'\ \ J
These rotations could be carried out with both the raw samples before calculating the covariances, and to averaged raw covariances. Let us consider rotation over a only, and define a = cosa and b =
since. Then the rotation of a covariance x y over a is given by
~x1yr = (ax' *by')(-bx' + ay') = -abx11 *(a2 -b2)x'y' *abyu (II.6)
-abx77* (a2 - b^xY + aby77
where the subscript r denotes the rotated covariance. However, when additional non-linear
transformations on r ' or y ' are carried out (such as detrending using a first- or higher order digital filter), the execution of these matrix transformations before or after computation of the covariances leads to different results (Krikke, 1994b). In that case it is recommended that the rotation operation is carried out on the raw data, rather than on the computed covariances.
The third rotation is carried out along the (rotated) u2-axis. The matrix M3 is given by
222 Sparse canopy parameterization^ for meteorological models
M,
1 0 0
0 cosß sinß
0 -sinß cosß
(II.7)
The angle ß over which the rotation must be carried out is found iteratively by specifying v3w3 from eq. II.7 and forcing it to zero:
v3w3 = -sinßcosßüjüj+sinßcosßa;2^2+(1 " 2 s ' n 2 ß ) t ' 2 a ; 2
= \v2v2 ~ w2wy -sinpcosp +.
(1 -2sin $)v2w2
—r-r v2v2 - w2w2
(II.8)
This leaves the need to find ß for which the term between square brackets is zero. This is made possible by introduction of a factor K, defined as
K u2w2
v2v2 - w2w2
Now eq. II.8 can be solved iteratively for ß, using
sß • / - /cos2ß + 8K2
sinß = (II.9) 4K
and cos ß + sin ß = 1. Usually three or four iterations are necessary to find ß.
• Frequency response corrections The turbulent flux density can be measured using eddy-correlation, provided that fluctuations
in the frequency range in which turbulent transport takes place are all sensed. In practice, this condition is hardly met due to a limited frequency response of the sensors and the data acquisition system, averaging over a path rather than taking a point value, separation between sensors for different quantities, and filtering applied. For each of these effects a theoretical co-spectral transfer function can be computed, which is unity for all frequencies for an ideal system. Convolution of this loss factor with the actual turbulent spectrum of the considered quantity gives a fraction of the true covariance that is actually sensed. Application of this method to really measured spectra will not be of much significance, since these spectra show the shortcomings of the sensor configuration we were looking to correct for. Therefore, theoretical spectra are used. The flux loss Af is then defined by
AF
F = 1
j"V n )VM ) d n
0
JV»)dn
(11.10)
where n is the frequency, T the net co-spectral transfer function, and S the theoretical co-spectral xy
distribution function. In the present analysis integration is carried out over a range of 0.001 < n < 100 Hz.
Moore (1986) worked out most of the frequency response correction for a Hydra flux measurement station (Shuttleworth et al, 1988). His work provided the basis for the correction algorithm developed here. The special corrections applicable to closed path sensors as the LICOR6262 have been obtained from Leuning and Moncreiff (1990). An overview of these corrections is also given by Moncreiff et al. (1995).
Digital sampling at limited frequency An analogue to digital sampling acquisition method causes aliasing of spectral contributions
exceeding the Nyquist frequency. The effective transfer function for an analog-to-digital sampling system, Ta(n), is given by
Instrumental aspects and data processing 223
T.<») 1 +
v " ' - " , « < nil (11.11)
with ns the sampling frequency. For eq. 11.11 it is assumed that aliasing is reduced by prefiltering the raw signal at n = njl, causing negligible co-spectral power above the Nyquist frequency. In spite of the limited application of low-pass filtering, eq. 11.11 was adopted (see Figure II.l for an example).
Figure II.1: Examples of the low-pass filtering transfer function Tv ( ) and the analog-to-digital transfer functioi Ta (•••••) for ns = 10 Hz
Low-pass filtering Low-pass filtering is applied to prevent aliasing, or folding frequencies higher than the Nyquist
frequency njl into lower frequencies (Stull, 1988). Electronic filtering using a 4rd order Chebychev filter was only applied to w-signals during EFEDA-I, from day 19 onwards, and not at all during EFEDA-II. The transfer function TJn) is given by
- l
Tv(n) (11.12)
where n0 is the cut-off frequency (at n s/2). The time constant of the filter is given by 1/2JC«0. Obviously, when no low-pass filtering is applied Tv = 1. An example of Tv is shown in Figure II.l.
Figure II.2: Example of the high-pass filtering transfer function Jd for ns = 10 Hz; shown are zd = 200 s ( ) and 600 s (•••••)
by
High-pass filtering (detrending) The transfer function Td(n) for a first order digital filter is to a very good approximation given
w (27! n t /
l + (2T[nx/ /a r f
n < n/2 (11.13)
An example is shown in Figure II.2 for xd = 200 and 600 s. For linear detrending the choice of the interval length is very similar to choosing a time constant
224 Sparse canopy parameterizations for meteorological models
zd for a running mean interval. However, for the linear detrending algorithms employed during both EFEDA campaigns no frequency response correction was applied.
Sensor response and tube damping The dynamic response of many sensors can be described by a simple first-order gain function:
Tr(n,vc) = [1+(2JCM)2X (11.14)
where lc is the time constant of the instrument. For most instruments this correction was neglected. Only the home-made thermocouples, the cup anemometers and the UCOR6262 were considered to have a low enough time constant to affect the measured frequency spectrum. The thermocouple time constants were estimated to be 0.5 s (as concluded from inspection of measured energy spectra, but higher than 0.1 s as cited by Van Asselt et ai, 1991). For the LICOR6262 0.2 s was taken. The time constant of the cup anemometers was given by Lu/u, where Lu was the response length (estimated as 1.2 m; Jacobs, personal comm.) and u the horizontal wind speed. An example is depicted in Figure II.3.
A special case of damping of fluctuations is caused by the tube transporting the air from the sonic anemometer volume to the LICOR6262 gas analyzer. Leuning and King (1992) present a transfer function T( given by
T,(") = Jexp(x / 6Dut)
2nnr, <10
D
elsewhere
(11.15)
where x is given by -(n n r()2 /, r( the tube radius, I the tube length, D the diffusivity of the gas being
analyzed and ut the air speed in the tube. Eq. 11.15 is strictly valid in cases where the flow within the tube may be considered to be laminar, and density fluctuations at all frequencies travel down the tube with the same velocity, uv Based on expressions presented by Philip (1963), Leuning and King (1992) state that this applies to frequencies for which 2itnrt /D < 10. For turbulent flow they propose the following transfer function
Tt(n) exp(-160Re"1/8r,n2; / uf) Re > Rec (11.16)
where Rec is a critical Reynolds number, equal to ± 2300, and Re is given by 2«(r(/v. Figure II.4 shows an example for both equations. For the corrections applied during EFEDA-II the laminar expression (eq. 11.15) was used, where rt was 0.0015 m, / = 4 m and ut approximately 5 m/s.
Figure II.3: Example of the sensor response transfer function Tr for ns = 10 Hz; shown are Tc = 0.1 s ( ) and 0.5 s ( )
Figure II.4: Example of the tube damping transfer function Tf; shown are eq. 11.15 for laminar flow ( ) and eq. 11.16 for turbulent flow (•••••). In both cases «s = 10 Hz, / = 4 m, r, = 0.0015 m, «, = 5 m/s and D = D„ = 2.56 10-* m2 /s
Instrumental aspects and data processing 225 i
Sensor line averaging In most cases a scalar quantity is measured over a (finite) path length rather than at a single
point. The effect of the spatial averaging involved can be described very well by
TP(P) 1
2*7 "o i i r\ A 1 - exp ( -2n ƒ) 3 + exp( -2 7t ƒ ) - 4 ±1.^—iL
2nj
(11.17)
where ƒ is the normalized frequency n plu, p being the averaging distance. Spatial averaging is relevant for all sensors. However, the effect on the temperature measured using a thermocouple is considered small enough to ignore a correction for this. The averaging path for the sonic temperature is equal to that of the vertical wind, and will be discussed hereafter. For the closed-path analyzer the averaging path is determined by the length of the gas chamber (0.15 m).
For the development of eq. 11.17 it is assumed that the averaging path is perpendicular to the average mean wind, which is true for each wind direction when the averaging path is oriented vertically. This applied to the configuration of the Lyman-a and thermocouple sensors during EFEDA-I. The Krypton in operation during EFEDA-II, however, was mounted horizontally. Graphical examination of the full formulation of eq. 11.17 given by Moore (1986) did not give rise to correct for this (see Figure II.5).
Figure II.5: Example of the transfer function for sensor line averaging for scalars, T„, for p = 0.025 m and w = 5 m/s
The effect of spatial averaging on measurements of vector quantities is different to that for scalar quantities. Moore (1986) gives a simplified transfer function for the vertical wind component, based on findings of Kaimal et al. (1968). The transfer function Tw for averaging the vertical velocity over a path with distance p reads
T,„ = _ 1 + exp(-27t/) 3 ( l - exp ( -27 t / ) )
4nf (11.18)
For the horizontal wind components a general function as eq. 11.18 is not possible to give, since it depends on sensor geometry and wind direction. Two different generalizations were carried out for the two experiments. For EFEDA-II eq. 11.18 was adopted for both the scalar and the horizontal wind quantities. The data of EFEDA-I were corrected using the original equations of Kaimal et al. (1968) and some assumptions about the instrumental configuration elaborated by Verhoef (priv. communication). For a symmetrical orthogonal set of transducers (as for the Kaijo Denki DAT310 device), the transfer functions were computed for a horizontal wind from a direction of 45° compared to each component. Then the sensor averaging transfer function can be reduced to a single function T : »
V sin;:/
*ƒ (11.19)
No attempt was made to investigate the assumptions leading to this formulation. For the DAT310 devices p = 0.20 m for all wind components, while p = 0.10 m for the Gill sonic anemometer. Figure II.6 provides an example of Tw and Tu.
226 Sparse canopy parameterizations for meteorological models
0.0001 0.001 0.01 0.1 n(Hz)
0.0001 0.001 0.01 0.1 n(Hz)
Figure II.6: Example of the transfer function for sensor line averaging for vectors: = T^ = Tu. In both cases p = 0.20 m and u = 5 m/s
Figure II.7: Example for the sensor separation transfer function T for s = 0.20 m and u = 5 m/s
Sensor separation Ideally, eddy correlation covariances are computed from measurements taken at exactly the
same point. In practice, usually a separation between different sensors is necessary. The loss of covariance due to sensor separation is a function of the distance between the sensors and the angle of the wind direction relative to the separation path. For practical purposes Moore (1986) developed a scheme which can be used to correct for both longitudinal and lateral separation, provided that the sensor separation s is small and open to the atmosphere:
T$(f) - exp(-9.9/15) <"-20>
where ƒ is the normalized frequency, given by n s/u (see Figure II.7).
Net transfer functions The net transfer functions for the several covariances can be found by multiplying the relevant
gain functions given above. A net transfer function for the data acquisition system, Tn, can be specified, which applies to all sensors. It is defined by
r„ = T„ Wv (11.21)
The net transfer functions for the separate variances and covariances depend further on sensor time constant xx, averaging path px, diffusion coefficient Dx and separation from the w-sensor s^.. The subscript x refers to vertical wind when x = w, horizontal wind in both directions for x = u, thermocouple temperature for x = T, sonic temperature for x = s, humidity measured by Lyman-a and Krypton for x = a, and humidity and C02-concentration measured by the closed path UCOR6262 device for x = h and c, respectively. Then the net transfer functions for the separate variances are given by:
T uu T
WW
T T m
Tu,vK) TJPv)
TxÂVw) Tp(pq)
rfr„)
(11.22)
Thh - T„ Tp(ph) I f o ) Tt(Dh)
Tec - Tn W r f o ) UDc)
while the covariance transfer functions read:
Instrumental aspects and data processing 227 i
ws ~ n vrPw' (11.23)
Twq = Tn TsK} fipfPj Tw<.Pw> Twk = Tn TsKh> W PW T«,<PJ TéPh) T«,c = Tn Ts(swc) Tr(xc) jTp(pc) Tw(pJ Tt(Dc)
Model spectra For the description of the atmospheric spectra and cospectra the formulations of Kaimal et al.
(1972) have been used. The formulations provide a description of spectral energy S as function of (normalized) frequency ƒ = n z/u and stability z/Lv, z being the measuring height. The spectra are derived for the variance of the three wind components and temperature, plus their mutual covariances. Moore (1986) concluded that spectra of the other scalars (humidity and C02) resembled the temperature spectra very well, and thus
Sqq = Shh = Scc = S 7T (TT.24)
$wq ' Swh = Swc = SwT
Furthermore, the spectra for both horizontal wind components are considered equal as well. The general function of Sxx under stable conditions (z/Lv > 0) can be represented by
"S**(») = ^-573 (11-25) Ax + Bxf
5'3
where Ax and Bx are functions of the atmospheric stability. Also the cospectra are well reproduced under stable conditions using a general equation:
tó«r(») " TT ( I L 2 6 )
A +B r 1
wx wxJ
Table II.l gives the formulations of Ax, Bx, Awx and Bwx.
Table II.l: Formulations of A^ Bx, Awx and Bwx for stable (co)variance spectra
Variance spectra Ax Bx
x = w Aw = 0.838 + 1.172 (z/L„) x = u Au = 0.2 A^ Bx = 3.124 Ax
1/3
x = T
Covariance spectra
X = M
x = T
AT = 0.0961 + 0.644 (z/L,,)06
Am
0.124 (1 + 7.9 z/Lvf75
0.284 (1 + 6.4 z/Lvf75
Bwx
2.34 Am
Unfortunately, the unstable spectra are not easily defined, due to a dependence on the boundary layer height z . Hojstrup (1981) developed suitable expressions for the horizontal and vertical wind velocity:
» ^ ( n ) - ƒ . WS 1 + 5 .3/ 5 / 3 (1 + 17/)5/3
C"1 (11.27) *—Til
and
1 228 Sparse canopy parameterizations for meteorological models
"S„„(") = 210/ f\
(1 + 33 / ) 5 / 3 Ç + 2.2/ 5/3 (11.28)
where
Cw = 0.7285 +1.4115 Ç C„ = 9.546 + 1.235Ê, Ç -2/5
/ W 3 2
2 V V
2/3
-L„
Since 2, was not known for most time intervals, a fixed value of 1000 m was chosen, as to represent a typical condition.
No suitable models for atmospheric temperature spectra for unstable conditions are cited in literature. However, Moore (1986) argued that for most conditions the spectra given by Kaimal et al. (1972) could be used. For the temperature variance is given
nSj^n) =
while the temperature cospectra read
5/3
14.94/
(1*24/)
6.827/ 5/3
[ (1 +12.5/)
4.378/ nSu,-M) =
1(1+3.8 / ) '
The spectrum of momentum transfer is described by
12.92/ 1375 (1+26.7/)
"S„»
20.78/
(1+31/)
12.66/
[ (1+9 .6 / ) 2
1.575
ƒ < 0.15
ƒ > 0.15
ƒ < 0.54
ƒ > 0.54
ƒ < 0.24
ƒ > 0.24
(11.29)
(11.30)
(11.31)
During daytime the correction as computed by eq. 11.10 was limited to a few percent for all the fast response eddy-correlation sensors. For wind speed measured with cup anemometers the corrections could be as large as 10%, as indicated by McBean (1972). The corrections were considerably larger under stable conditions, as the contribution of high frequencies to the turbulent exchange becomes more significant. However, since the fluxes are then generally small, the absolute significance of the assumptions specified above is not too large.
Based on these theoretical spectra and the transfer functions described above, Figure II.8 gives
an example of the net frequency response corrections applied to au and to w T , for a specified height and wind speed.
• Various aspects related to fast response measurements Apart from the rotation and frequency response corrections some other aspects play a role for
the interpretation of the measurements by fast response sensors. We discuss here the quantity actually measured by a cup anemometer, sonic thermometry, and open- and closed path humidity sensors.
Vector averaging of cup anemometers Since a cup anemometer cannot discern between various wind directions it measures the
average vector wind speed U, rather than the total wind speed in the direction of the average wind,
Instrumental aspects ana data processing 229 i
u. Bernstein (1967) elaborated a relationship between u and IF, which is a function of the standard deviation of the horizontal angle a:
ïï = TTexp(-0.5o-2) <"-32>
Van den Hurk and de Bruin (1995) derived expressions for the relationship beteen au and au:
(11.33)
A -TT' exp (wj-
In theory, a must be measured at the same height as the cup anemometer. In practice, however, it is only determined at a single level and assumed to be constant with height over the entire wind profile. Here, aa is measured by the sonic anemometer at 4.35 m height during EFEDA-I, and by the wind vane at 10.2 m during EFEDA-II.
Figure II.8: Example of frequency response corrections as function of z/L: -AF„, •AF„, Configuration parameters are as follows: z = 10 m, « = 5 m/s, pu = pw = 0.20 m, swT = 0.25 m, zc = 0.5 s (thermocouple) and ns = 10 Hz
Sonic temperature The temperature obtained by the sonic anemometer (eq. 2.4) needs to be converted to a physical
air temperature using the specific humidity. Schotanus et al. (1983) have demonstrated that the variance of the sonic temperature and the vertical flux density can be written as
4 T W
1.02 TT'?
ATüu'T'
- 0.512 T rj2 •
•2.04 T uuq
(11.34)
and
son w'T' = iw'TL.-0.51 T r ö y T uu w (11.35)
respectively. During EFEDA-I and EFEDA-II measurements of the open path hygrometer (Lyman-a and
Krypton) mounted near the sonic anemometer were used to obtain q. In particular for the systems 1, 3 and 4 in use during EFEDA-I this value is doubtfull and likely too low. During EFEDA-II, comparisons between psychrometer and Krypton results showed that the Krypton gave very reliable values of q. Furthermore, the correction to the variance of the sonic temperature was limited to the first three terms on the right-hand side of eq. 11.34.
Webb-correction
As pointed out by Webb et al. (1980), the average vertical velocity w is unequal to zero when there is a sensible heat flux between the surface and the atmosphere. The vertical flux density of dry air can be written as
230 Sparse canopy parameterizations for meteorological models
"Pa = w Pn+W'pa = ° (11.36)
Since according to the Boussinesq approximation /
P. .
Ta (IÏ.37)
the average vertical velocity can be obtained from eq. 11.36 and is given by w'T' I T. This mean vertical wind affects the turbulent flux density Fc of any scalar density pc, given by
Fc = wpc+w'pc = -l.w'T' + w'pc (11.38)
This so-called Webb-correction applies to any scalar whose density rather than its mixing ratio
r = p c /p n is measured. It can be shown that p~aw r is approximately equal to Fc, in which case the
Webb-correction disappears. The situation is a little more complicated for air mixtures, as moist air. Considering the air as a
mixture of dry air and water vapour with density pv, the mean vertical wind velocity is given by
_ mawPv w =
mv Va i+fz£!i w'T' (11.39)
which implies for Fc
wp +w p ma wPv —
—Pc + wT 7~T — - p c + w p c
T
(11.40)
For water vapour pc = pD, and eq. 11.40 can be rewritten as
F„ = + mvVa
\ J
w pv + -—wT T
(H.41)
The Webb-correction applicable to open path sensors can be as large as several tens of percents, depending on the sensible heat flux density. Leuning and Moncreiff (1990) show that the Webb-correction for a closed- path system as the LICOR6262 is limited to a few percent by bringing the sampled air to a common temperature. By this procedure a major part of the correction associated
with the sensible heat flux density (equal to ( l / T ) p c t u T ) vanishes. This gives
ma ™Pv — ^ P c
Plmv
wT T1 ——pc+wpc
T
(11.42)
and
1 + ™ a P ç
K* mvP~a w'pv
(11.43)
for the LICOR6262 C 0 2 and water vapour flux, respectively. However, an extra correction accounting for the different temperature and air pressure in the chamber compared to outside conditions has to be introduced. This correction is automatically carried out by the LICOR device.
LICOR signal delay The closed path LICOR6262 sensor detects gas concentrations in air, after a transport through a
Instrumental aspects and data processing 231
sampling tube. This transport takes some time (in the order of 2 s for 4 m tube). For the EFEDA-II data the delayed signals of pv and pc measured by the UCOR626 device were shifted in time. The time
interval was defined as the time delay for which the covariances pvTson and p e r were maximal (McMillen, 1988).
Oxygen absorption by Lyman-a and Krypton The instrument response of the Lyman-a and Krypton humidiometers, given by eq. 2.5, is based
on the assumption that water vapour is the only gas absorbing light at the monochromatic wavelength being detected. However, in practice some other gases (in particular oxygen and ozone) are not entirely transparent at the Lyman-a and Krypton wavelengths. Particularly the contribution of oxygen is of interest, as it is present in much higher concentrations than water vapour. For the present analysis we ignore other gases than oxygen.
A more general formulation of eq. 2.5 includes the contribution of other gases to light absorption:
1 = IOeXP-dsE-T-PiO
(11.44)
where ^ is an absorption coefficient of gas i at standard pressure, and the received light is assumed to be monochromatic. The humidity fluctuations pv' measured by a Lyman-a or Krypton can be expressed as function of the signal fluctuations linearized around the mean signal (see section 2.2.4). Then it can be shown that
''"iTr-T'' (IL45)
dkvI kv
where the subscript o refers to the oxygen concentration and absorption coefficient. Referring to eq. 11.37, the oxygen concentration fluctuations can be approximated by
r0 o
where C0 is the relative concentration of oxygen (21%) and m0 its molecular weight. This yields for the latent heat flux density an expression where the oxygen contamination is represented by a sensible heat flux density:
-TT ITT ComoVK-rp m 4 - , W p „ = - + wT (11.47)
" dkj RT2 K For a Krypton KH20 hygrometer kv = 0.143 and k0 = 0.0085. The absorption coefficients at
Lyman-a are a little more favourable for the detection of water vapour: kv = 0.481 and k0 = 0.00049. All these coefficients are slightly temperature dependent. Only the value of k0 for the Krypton wavelength gives rise to carry out a correction according to eq. 11.47.
Surface temperature and radiometer corrections
• Surface temperature The radiometric surface temperature is obtained from the measurement of longwave radiation
in the range 8 -14 urn emitted by a surface. The relationship between body temperature and measured radiation depends on the radiation frequency range and surface emissivity. The total radiation emitted by a black body of temperature T is given by oT% where a = 5.67 10"8 is the Stefan-Bolzman constant. However, the radiation emitted in a limited frequency range deviates from this law, and can be approximated by a'r. Around X = 12 am 6 = 4, but for the range 8 -14 urn a = 1.25 10"9 and b = 4.5.
In the longwave frequency range many surfaces don't behave as a black body. This implies that the total amount of emitted radiation is less than &F, and this is usually expressed using an effective emissivity e, defined as
2 3 2 Sparse canopy parameterizations for meteorological models
Je(X) MxdX (11.48)
rT4
where M^ is the emittance of the body at wave length X. Most radiative temperature sensors include a correction for an emissivity < 1. However, downward radiation reaching a surface is partially reflected when e * 1, and observed by the radiation sensor. An expression for the correct surface temperature Ts as function of the measured value Ts m, and the surface emissivity assumed by the sensor £T is given by
\l/b
£TaTsbm-(l-t)Ltu (11.49)
T. =
where L%_14 is the downward radiation in the wave length length range 8 -14 \xm. For EFEDA-I we assumed e = 0.993 for the plants, 0.973 for the bare soil and 0.98 for the surface seen by the high sensor (Bolle and Streckenbach, 1992). The sensor emissivity was kept at unity for all sensors. L8.14 is usually not measured directly. Here, we used the semi-empirical expression developed by Idso (1981), reading
^8-14 0.24 + 2.9810" i 2 eflexp
3000 a r : + 60 C (11.50)
where ea is the vapour pressure at reference height, specified in mb, Ta the air temperature, and C the cloud cover. In practice, L 8.14 as given by eq. 11.50 is about 40% of the total incoming longwave radiation.
• Obtaining temperature of separate surface components from cable temperature The temperature measured by the sensors running over the two horizontal cables were
corrected for emissivity and reflection as indicated above. Moreover, some strategy was developed to derive the bare soil temperature, the plant temperature and a weighted average of these from their results.
15 20 distance (m)
10 20 » 40 50 frequency (%)
70 80 90 100
Figure II.9: Time series of surface temperature measurement from the low cable, DOY 163,14:10 GMT. Shown left is the observed temperature series, and right the cumulative frequency distribution.
A common temperature signal measured by the low cable during daytime is shown in Figure II.9. The difference between the cool plants and warm soil is clearly seen. The cumulative frequency distribution is shown as well. For each time slot the average bare soil temperature was defined as the 95% percentile value of this cumulative distribution. A percentile value < 100% was chosen, in order to ignore incidental high extremes. The exact choice of the percentile value is rather insignificant for the bare soil temperature, as can be seen from Figure II.9. The cool end of the distribution shows a much steeper slope, caused by the partial transparency of the plants. A quite arbitrary 5% percentile
Instrumental aspects and data processing 233
value was chosen as to define the plant temperature of the sample. A weighted average of the surface temperature was found by relating each temperature reading
from Figure n.9 to an effective area. From a set of figures equivalent to Figure n.9 an estimation was made of the position and radius of the plants underneath the cable. These dimensions were found around day 20, and plant growth was not taken into account. The effective area at of each measurement position within the radius of a plant was considered to be equal to half an arc with width equal to the distance between two measurements (see Figure n.10). Temperatures outside the radius of the plant were regarded to be representative for the bare soil area between the plants and equally weighted. The average surface temperature Tsur was thus defined by
EV T = sur E«,
(11.51)
sensor line
Figure n.10: Schematic representation of representative area per surface temperature sample, indicated by the heavy dots on the sensor line. The shaded plant area represents the area a, representative for the measurement point indicated by the arrow. The lowest panel shows a schematic record of the measured surface temperature
• Shading of incoming shortwave and diffuse radiometer The incoming radiation sensor applied in EFEDA-II was shaded by the mast early in the morning.
Data in the time slots where this occured were replaced by linear interpolations of the neighbouring time slots. Due to the virtual absence of clouds at all days this procedure could be applied safely, and was estimated to give an error of less than 5%, valid for low values of K . The sensor detecting reflected shortwave radiation in this experiment received a considerable amount of radiation reflected by the mast at about 15 GMT each day. This was corrected for by reducing K at this time by a fixed percentage, which was also obtained from the interpolation of neighbouring time slots, measured at several cloud-free days spread over the whole period.
The diffuse radiation was increased by 12% to account for the hemispherical radiation blocked by the shadow ring, following the instructions in the shadowring manual.
• Difference between longwave and shortwave sensitivity of net radiometers The longwave radiation measured by the allwave Schülze-Däke sensor applied in EFEDA-II can
be corrected for the difference of sensor sensitivity to short- and longwave radiation. When the incident shortwave radiation is known (measured separately) the corrected longwave radiation is given by
xtV-*•! 1 4 (11.52)
where V is the voltage measured, xl and xs the gains for longwave and shortwave radiation respectively, and zb the body emissivity, which is assumed to be unity here.
234 Sparse canopy parameterizations for meteorological models
4 Soil heat flux density corrections
The soil heat flux density measured using soil heat flux plates is subject to three major sources of error: a non-ideal heat transfer to and through the plate, heat storage in the soil layer above the plate, and ignoring energy transported across the heat flux plate as latent heat.
Non-ideal heat transfer is associated with a poor contact between the soil plate and the surrounding medium, and a difference between the heat conductivity of the plate and that of the soil. A correction factor c^ for the conductivity difference is given by (Philip, 1961)
= 1 -OL V
1 V M , 1- — (11.53)
where cc is a factor depending on the shape of the heat flux plate (equal to 0.57t(8/37t) = 1.70 for circular plates), à the thickness of the plate (= 4 mm) and A the areal surface (177 cm2). The soil heat conductivity XT was estimated as discussed in section 2.2.5. The conductivity of the plates X was given by the manufacturer. No correction was carried out to account for the poor contact between the sensor and the soil.
The heat storage above the plates was computed similar to the determination of the soil heat flux density by the caloric method (eq. 2.18), where obviously only the change of heat content in the layer between the surface and the installation depth of the sensors is considered. This correction can modify the measured fluxes by more than 100 W/m 2 .
For the soil heat flux density computed from the caloric method the temperature rise at the deepest level gives rise to uncertainties in the calculated fluxes. The temperature at 50 cm showed a significant rise during the measurement campaign, and the zero-flux condition at the lower boundary is thus not met. Since no direct measurement of the soil heat flux density at a depth of 50 cm were carried out, no correction could be applied for this.
For each layer and each measuring day p'Ch was computed using eq. 2.21. For practical purposes the value of p'Ch linearly increased with depth from 10 cm onwards. Also, a linear regression was carried out to account for the temporal change at all levels (see section 2.4.4 for details).
Upward latent heat transfer across the plate may lead to an overestimation of G. This transfer may take place when evaporation occurs below the heat flux plate (Mayocchi and Bristow, 1995). This effect was ignored in the present study.
Instrumental aspects and data processing 235
Appendix III: The bulk leaf boundary-layer resistance
The leaf boundary-layer resistance rb is the resistance encountered by a scalar when it is transported from the leaf to the ambient air, or the other way round. The resistance describes the transport through a thin laminar sublayer immediately surrounding the leaf. This layer is an internal boundary layer, caused by the wind blowing over the leaf. The thickness of this layer therefore depends on the drag forces exerted on the leaf (wind speed) and on the typical size of the leaf. For small leaves, the laminar boundary layer has no chance to develop when the leaf is exposed to wind, and the leaf boundary resistance will therefore be smaller. In general the leaf boundary resistance is given by the semi-empirical expression
lw III.l ru=a
N "(z)
The coefficient a is not dimensionless, and holds for lw expressed in m and u in m / s . The coefficient is obtained by analysis of dimensionless quantities governing the flow through
the laminar sublayer surrounding the leaf. It is valid under the following assumptions: • the flow in a small layer just over the leaf is laminar. Then the Nusselt number Nu, which
defines the ratio of the thickness of the laminar sublayer 8 to the characteristic size of the leaf lm, is a function of the square root of the Reynolds number Re, defined by u lw/v, with v the kinematic molecular viscosity
• the temperature is uniformly distributed over the leaf. In this case, Nu can be expressed according to
Nu = !l= 0.66 Pr033 Re05 «"-2) 5
where Pr is the Prandtl number, defined by the ratio of the viscosity and thermal diffusivity of dry air (equal to ± 0.71)
• the exchange of heat occurs at two sides of a leaf • an excess conductance is caused by buoyancy effects and extra generation of turbulence at the
curled edge of the leaf, causing an increase of the coefficient in eq. III.2 to ± 1.08. • no additional corrections are applied to account for mutual sheltering by leaves (see section
3.2.3)
Under these assumptions eq. III.l can be obtained by solving the equation
H _ Pcp _ K AT " r , L
f \
!i 5
V /
(III.3)
where Xa is the thermal conductivity of air. The total resistance of a layer of leaves is inversely proportional to the total leaf area in that
layer dL, expressed by
rAdl) - 1 . <I"-4> bK ' dL
The leaf boundary resistance will generally be a function of height, due to the dependence on dL and
• 236 Sparse canopy parameterizations for meteorological models
M(Z). Therefore, in cases where a vertical canopy has to be condensed to a virtual source at a single level, a proper vertical average value for rb must be obtained. This averaging procedure is quite straightforward for cases where profiles of u(z) and dL are known. In that case the total boundary resistance valid for a canopy is obtained by an inversed addition of all resistances in each layer, when these resistances may be thought to be connected in parallel. For infinitly thin layers, the bulk leaf boundary-layer layer resistance ra
c is given by
(III.5)
LAI
where LAD(z) is the leaf area density at height z. The integral is taken over height z rather than over total leaf area LAI, to express the functional dependence of rfc on u(z).
For larger scale approximations the detailed information about LAD(z) and w(z) is generally not available. Therefore, some approximation to eq. III.5 is required. Here, the integrated resistance is computed for a large range of canopy structures and wind profiles. The computed resistances are then expressed in terms of the parameters which are assumed available, i.e. the friction velocity u„ the characteristic leaf size lw, and the total leaf area LAI.
The within canopy wind profile is assumed to obey an exponential decay:
u(z) = u(h)exp z -«„ —
"h
(III.6)
where u(h) is the wind speed at canopy height h, and au is an extinction coefficient, depending on the canopy structure, plant spacing etc. A value of 2.5 - 3 is often taken for agricultural crops. The wind speed at z = h is evaluated using the adiabatic logarithmic wind profile:
u(h) = In K
h-d
'Om
(III.7)
In order to give a general expression for eq. III.5, d and z0m are assumed to be a fixed portion of the canopy height, i.e., d/h = 0.63, and z^/h = 0.13.
The distribution of leaves with height was simulated using a Beta-distribution, given by
ß(x) '"T" '-X? n ~ l V ' <p*q-l)\jf-1(l-xf (III.8) (p -!)!(<?-!)!
in which two integer parameters p and q determine the shape and the value of x where ß(x) is maximum. The Beta-distribution resembles the Poisson distribution, but its integrated value in the range [0 -1 ] is always unity.
Eq. III.5 was evaluated with a great range of parameters. The friction velocity u, varied from 0.05 to 0.8 m / s , LAI from 0.1 to 3.5, lw from 0.01 to 0.2 m, and a„ from 1.5 to 3.5. The Beta-distribution was varied using p = 2,4 and 6, and keeping q constant at 2. p = 2 corresponds to an almost hemispherical distribution with the maximum leaf area at z/h = 0.5, whereas p = 6 shows a maximum LAI at z/h = 0.83. A total of 432 cases was surveyed.
The best fit of this sample on eq. III.l was obtained by adopting
97 •\J u*
(IH.9)
LAI
For the set of variables used here the correlation coefficient was 0.95. The formulation corresponds best with p = 4 and au = 2.5. For p = 2 eq. III.9 underestimates the
analytical integration by ± 12%, whereas for p = 6 it is overestimated by this amount. For the latter case the integrated resistance is reduced by the convolution of high leaf area densities and high wind speeds near the top of the canopy. When the different leaf area distributions are distinguished, and the factor preceding eq. III.9 is changed accordingly, the correlation coefficient is as large as 0.999 for all cases.
The bulk leaf boundary-layer resistance 237 i
Appendix IV: The photosynthesis model at the leaf scale and calculation of ambient conditions
Using eq. 3.33 the leaf stomatal conductance for water vapour transfer, gs, can be defined as the ratio of net assimilation rate A„ and concentration difference C„ - C,:
i< A" (IV.l) C -C
provided that the cuticular conductance can be ignored, as was assumed here. Additional models for An and Ct/Cs are necessary to complete eq. IV.l.
At low radiation levels the net assimilation rate An can be regarded as a linear function of the light intensity:
\-*ih-*i (IV-2)
where la is the intensity of the intercepted PAR, Rd the dark respiration and e, the initial quantum use efficiency. At high light intensities An approaches an asymptotic value, Am. In these conditions, the C02-concentration is the limiting factor for photosynthesis. An empirical asymptotic exponential function, as proposed by Goudriaan et al. (1985), is used to describe An at both low and high light intensities, thereby including the limiting effect of both light and C0 2 :
An^Am+Rd) P - e x P f -e,I. Ï A„+R,
R ( I V - 3 )
Rd
The initial quantum use efficiency e; is affected by photorespiration, and may be calculated as (Goudriaan et al., 1985)
C - r e, = e 0 _ ! (IV.4) ' ° c + 2 r
where e0 is a maximum efficiency (= 0.017 mg/J PAR for C3 plants), and T is the C 0 2 compensation concentration, being the equilibrium C02-concentration which is achieved when an illuminated leaf is placed in a closed chamber. The gross assimilation is then balanced by the respiration processes, and net photosynthetic rate An will be zéro. T is mainly affected by the photorespiration and approaches 0 for C4 plants. For C3 plants under the current 02-concentration it depends mainly on leaf temperature T;. This dependence can be described using a Q10-response function, according to
2 3 8 Sparse canopy parameterizations for meteorological models
T ( I V - 5 )
where T(25) is the value of T at T, = 25°C, equal to 45 umol/mol for C3 plants. Q10 is taken 1.5 for T. At low values of Cir Am is linearly related to the C02-concentration according to
where gm is the mesophyll conductance. At higher values of Ct, Am is asymptotically bounded by a maximum rate, Am m a x , related to the ability of plants to allocate the products of the photosynthesis process. Am is taken as
Am "Awn« H - « ? (-*»«:,-nï V
A
m,max
(IV.7)
An expression for Am m a x as function of leaf temperature applicable to Vitis Vinifera was expressed following Collatz et ah (1992), reading
'T, -25
A
m,max j l + exp ( 0.3 (Tj - T,))} j l + exp ( 0.3(1, - T2))}
where Am max{?5) = 2.2 mg/m 2s , Q1 0 = 2, and T3 and T2 are reference temperatures, taken in this study as 15 and 42°C, respectively (Jacobs, 1994). Rd is estimated as Am/9 (Van Heemst, 1986).
The mesophyll conductance gm can be derived from the light saturated rate of photosynthesis. gm can be expressed using a function equivalent to eq. IV.8, with gm(25) = 2 mm/s , Q10 = 2, T3 = 0°C and T2 = 42°C, respectively (Jacobs, 1994).
Goudriaan et ah (1985) observed a fairly conservative ratio of Ct/Cs. A slightly modified ratio,/, is used to compute Cs - Cf.
C - r _ ! = f (IV.9) C-T J
Note that using eq. IV.9 Ci/Cs -> 1 as An -> 0. ƒ may be fairly conservative, with a value of 0.7 for C3 plants (Goudriaan et ah, 1985).
Jacobs (1994) incorporated an effect of air humidity on gs by assuming t ha t / i s a linear function of the ambient humidity deficit, Ds:
/ = /o 1 - ^ i (IV.10)
where a minimum assimilation rate, corresponding to a situation where stomata are fully closed but C 0 2 is supplied through cuticular conductance, is ignored. For the present species, Jacobs (1994) found Dmax = 58.2 g /kg and f0 = 0.916. In this study the value o f /was not allowed to exceed a maximum value of 0.85, taking the average of the range 0.8 - 0.9 reported by Morison and Gifford (1983). The modification caused a typical maximum value of gs (full sunshine, leaf temperature below 35°C) to be about 20 m m / s rather than 30 mm/ s without constraint. This latter value is rather high compared to values reported by for instance Choudhury and Monteith (1986), which justifies this modification. The values of the calibration coefficients in eqs. 3.36 and 3.37 partially depend on the maximum value for ƒ
According to eqs. IV.9 and IV.10, C, will never exceed Cs. This implies that application of eq. IV.10 together with eq. IV.l can yield negative conductance values, because An becomes negative as
The photosynthesis model at the leaf scale and ambient conditions 239 •
Ia -* O due to dark respiration (see eq. IV.3). In practice the correlation between An and gs is difficult to establish under conditions of low assimilation rates, since the C02 concentration gradient will likely be very small. In this study gs was simply assumed to be zero when An < 0.
The value of the specific humidity deficit at the leaf scale, D$, was obtained by extrapolating the deficit profile to a hypothetical source level at z ^ + d. A specific humidity at leaf level, qc, is obtained according to
*£ = 9 .*f ('«•':) ( i v n )
where E is the measured evaporation rate above the canopy, ra given by ua/u,2, and rac parameterized
according to eq. HL9. A humidity deficit was calculated separately for shaded and sunlit leaves, by taking the measured average leaf temperature in each light category to specify qsat.
The amount of absorbed PAR, Ia, was calculated according to eqs. 3.39 and 3.40 for shaded and sunlit leaves, respectively.
2 4 0 Sparse canopy parameterizations for meteorological models
Appendix V: Numerical aspects of the SVAT-models
The computer program in which the coupled SVAT-PBL models were coded consisted of two modules: the PBL- and the SVAT-module. The coupling was carried out at the level zR, which united the lowest PBL-gridpoint and the reference height of the SVAT's. During each time step first the SVAT-module computed the surface fluxes, followed by a calculation of the PBL-profiles and -height by the PBL-module, generating a new reference temperature, specific humidity and wind speed at zR.
The SVAT-module contains various parameterizations, as outlined in section 4.1. This appendix describes the program flow of the SVAT-module, for each of the cases described in chapter 6.
• The reference model The sequence of steps to solve the surface energy balance in the reference model closely follows
the suggestions made by Deardorff (1978), and is as follows: 1 specify the crop resistance, using environmental variables at canopy height of the previous
timestep 2 compute aerodynamic resistance above canopy (ra
a) and u. iteratively from ua and 6a - QQ, with 6fl from the previous time- or iteration step. Calculate the aerodynamic resistance to the soil surface (rfl
s) and to the canopy surface (rflc)
3 calculate qs
4 compute new value of 80 and q0
5 calculate leaf temperature 8„ specific humidity qc, and canopy evaporation fraction \ from radiative input and 90 and q
6 update q0 and repeat step 5 until convergence of 6C
7 calculate canopy and soil fluxes, and repeat from step 2 onwards until convergence of rj" 8 compute a new value of w^ew
9 calculate surface and deep soil temperature from G using the force-restore scheme 10 calculate surface and deep soil moisture content from ģs and XEC using the force-restore
scheme
• The case 'big leaf' For the case Trig leaf' the program flow is slightly different than the reference model:
1 as in the reference model 2 calculate r" as in the reference model, but with 80 equal to the temperature extrapolated to z0m
3 open Newton-Raphson iteration for Tsur according to
Q , - G - p X — + Pcp ;
T = Ty - —— (V.l) sur sur - N
v ' -4eaT s
3„ r -2Cv^ 1 2JC . s (P/Pof286
• P*- + pCp
where T^ur = T$ur from the previous timestep, and C = p'C^dj. rQ, Q», G and C are given by eqs.
4.4,4.7, 4.8 and 4.48, respectively. Use is made of the linearization of Tsur to
4 ( 0 3 (Tsur - Tlur). estimating qsat(Tsur) by qJJ^ * s(Tsur - T^), and discretizing dTsur/dt
a s ( T ( I 0 . - T f j / A i .
Numerical aspects of SVAT's 241
4 repeat steps 2 and 3 until convergence of ra° 5 compute surface fluxes from final values of Tsur and r° 6 calculate surface and deep soil temperature from G using the force-restore scheme 7 calculate surface and deep soil moisture content from XE using the force-restore scheme, taking
• The case 'isotherm' The numerical scheme in the case 'isotherm' resembles the 'big leaf' case, in that they both solve
the energy balance equation for the surface temperature. The numerical scheme reads: 1 as in the reference model 2 specify the fraction of surface covered by the skin reservoir, C; 3 calculate ra" as in the case T)ig leaf' 4 solve for T$k by rewriting a modified version of eq. 4.15 in terms of Tsk, and linearizing Tsk*,
dTsk/dt and s using Tsk from the previous time- or iteration step. The modification consists of replacing the expression for the soil heat flux (eq. 4.14) by the force-restore expressions, as applied in the case 'big leaf' (eq. 4.8).
5 repeat steps 3 and 4 until convergence of H 6 compute surface fluxes from final value of Ts)c and ra
a, using the explicit values of C; and oy 7 calculate surface and deep soil temperature from G using the force-restore scheme 8 calculate surface and deep soil moisture content from XES and XEC, using the force-restore
scheme
• The case '3 fracs' The case '3 fracs' is similar to the previous case, except that the skin temperature is established
for each surface fraction separately. The final scheme is given by: 1-2 as in the case 'isotherm' 3-6 as in the case 'isotherm' by taking C( = 0 and oy = 0 (soil only) 7 as 3-6 by taking C; = 0 and oy = 1 (vegetation only) 8 as 3-6 by taking C; = 1 (skin reservoir only) 9 compute the average surface fluxes Q,, H, XE and G by weighing the fluxes from steps 3-8 as in
eq. 4.18 10 calculate an average skin temperature and friction velocity according to the same procedure 11 calculate surface and deep soil temperature from G using the force-restore scheme 12 calculate surface and deep soil moisture content from XES and XEC, using the force-restore
scheme
• The case 'aero D78' The case 'aero D78' is almost equal to the reference case. The only difference is the formulation
of ras and ra
c in step 2.
• The case 'aero MH95' The numerical scheme in 'aero MH95' also resembles the reference model:
1 as in the reference model 2 compute u» from ua and a dimensionless far-field resistor, 9?n
fl. Since 9?a" corresponds to a reference height of 2h, it is not equal to the total resistance between z ^ and zR. An extra resistance including a stability correction "P^ is applied for the range between 2/J and zR:
K In
2h v /
2h
L. v 'J v ' /J
(V.2)
with Lv from the previous time step. This implies a stability correction between 2/i and zR, but not below 2h. Calculate the aerodynamic resistances ra", ra
c, ras and rn from a, and the
dimensionless resistance coefficients. The resistances are equal for heat and moisture transfer, and ra
a and ras are computed using the flux partitioning of sensible heat. rn is incorporated by
adding its value to rac
3-10 as in the reference model
242 Sparse canopy parameterizations for meteorological models
• The cases 'rc C 0 2 ' , 'rc VB95' and 'rc fix' The numerical sequence of the cases 'rc C0 2 ' , 'rc VB95' and 'rc fix' are equal to the reference
model. The ambient conditions used to parameterize the crop resistances are taken from the previous times tep.
• The case 'rc big C0 2 ' The case 'rc big C 0 2 ' is similar to the case 'big leaf'. The humidity deficit is evaluated using the
specific humidity at z0m and the average surface temperature.
• The case 'soil VB95' The case 'soil VB95' utilizes a similar numerical scheme as the reference model, except that the
steps 9 and 10 are replaced by a solution of the diffusion equations for temperature and soil moisture: 1-8 as in the reference model 9 calculate a new soil temperature profile using a locally implicit scheme (Viterbo and Beljaars,
1995). The diffusion equation (eq. 4.9) is discretized as
n*\ n
n / r ' ' °u>~0;,f (v.3) p C " — I t — - - — ; —
in which i indicates the spatial coordinate and n the time level. G, ( and Gi b are the heat fluxes at the top and bottom of soil layer i, respectively, discretized as
(V.4)
(V.5)
G u -',b
G , -'/'
*T,i+l/2
"*T,!-l/2
0 . 5 ( Z / + z M )
T"*1 -Tn
DC Cr. . 4-r.l
For XT the 'upstream' values are used (see section 4.1.2) 10 calculate C;
11 specify the root extraction and surface infiltration rate 12 calculate the new soil moisture profile from eq. 4.11 using a global semi-implicit scheme
(Viterbo and Beljaars, 1995):
n+l n _* » ^i ~Wi _ ti*\/2-ti-l/2 n e (V.6)
" ; + Pjo!'<a,i At
where the moisture fluxes F are given by
i"i+l/2 = 'P^H,M/2a5 (2 j+Z j t i )-VH,Hl/2 (V.7)
and the moisture content is made implicit by
CO; = 1.5(0,- + ( 1 - 1 . 5 ) 0 ) , l v - ° '
• The case 'soil rss'
The program flow in the case 'soil rss' is similar to the reference model. The relative humidity at
the soil surface is specified by eq. 4.83, and the specification of q0 (equivalent to eq. 4.56) is carried out be replacing ra
s by ras + rs
s.
Numerical aspects of SVAT's 243
• The case 'soil CM88' In the case 'soil CM88' the entire surface flux partitioning is calculated using the scheme of
Choudhury and Monteith (1988). No iterations are included: 1 as in the reference case 2 calculate the soil evaporation resistance rs
s according to eq. 4.82 3 calculate ra" and u. according to Louis (1979), and ra
s and rac as in the reference model
4 specify Q,^ and Q.c using the exponential decay (eq. 4.65) 5 solve the temperature and humidity at the soil surface, canopy surface and canopy air layer
with the forcings at reference height, and the specified resistance and net radiation values 6 calculate surface energy balance components and update iuiem
7 calculate new deep soil temperature 8 compute soil moisture content in top layer and bottom layer using force-restore 9 calculate new depth of upper soil layer
2 4 4 Sparse canopy parameterizations for meteorological models
Appendix VI: Values of surface and boundary layer parameters, calculated with the reference SVAT coupled to the PBL-model
This appendix includes the absolute values of the quantities calculated by the reference runs that were analysed in chapter 6, and listed in Table 6.6. For the seven surface types listed in Table 6.2, the daytime surface and entrainment fluxes, and the PBL-height, temperature and specific humidity at specific times are listed in Table VI.l for the MLS initialization, and in Table VI.2 for DRY.
Table VI.3 lists the reference values in case of the simulation of EFEDA-observations, for which the measured surface fluxes were taken as reference. Also shown are the values calculated using the reference SVAT coupled to the PBL-model.
Table VI.l: Values of analyzed parameters calculated using the reference SVAT coupled to the PBL-model for the MLS initialization
quantity
Q.D(dayl74)
HD (day 174)
XED (day 174)
GD (day 174)
H,D (day 174)
XEtD (day 174)
z,12 (day 174)
z-18 (day 174)
z,6 (day 175)
W 8 (day 174)
8„IS (day 174)
B/"" (day 175)
q18 (day 174)
Hmin (day 175)
units
W/m2
W/m2
W/m2
W/m2
W/m2
W/m2
m
m
m
mm
°C
°C
g/kg
g/kg
vineyard
319
185
37
97
-4
154
1268
1796
50
-0.66
29.9
18.6
9.5
10.3
vineyard o> = 0.4
349
166
104
78
A
166
1262
1712
50
-1.86
19.6
17.7
10.2
10.7
vineyard oy=0.7
366
158
148
60
-3
182
1268
1691
50
-2.58
29.5
17.2
10.7
10.7
vineyard a, = 1.0
370
151
178
42
-5
193
1278
1672
50
-3.12
29.4
17.2
10.9
10.8
vineyard on clay
315
196
55
64
•4
173
1365
1873
52
-0.96
30.1
16.5
9.5
9.5
tigerbush
355
200
81
73
-4
183
1369
1874
52
-1.44
30.2
17.0
9.7
10.4
forest
338
187
64
87
-3
166
1255
1781
50
-1.14
29.9
16.5
9.7
10.2
Absolute values of coupled SVAT-PBL runs 245
Table VI.2: As Table VI.l, for the DRY initialization
quantity
Q.D (day 174)
HD (day 174)
\ED (day 174)
GD (day 174)
HP (day 174)
XE,D (day 174)
z,]2 (day 174)
z,18 (day 174)
z,6 (day 175)
AoM (day 174)
e,1« (day 174)
8/11'" (day 175)
cfe (day 174)
cf'n (day 175)
units
W/m2
W/m2
W/m2
W/m2
W/m2
W/m2
m
m
m
mm
°C
°C
g/kg
g/kg
vineyard
291
129
57
105
-4
43
1195
1651
50
-1.02
32.5
17.5
4.7
6.6
vineyard af=0.4
325
99
139
87
-5
82
1122
1495
50
-2.46
31.9
17.2
5.6
8.8
vineyard a, = 0.7
346
84
194
68
-6
108
1107
1434
50
-3.42
31.6
17.2
6.2
9.6
vineyard of =1.0
352
74
230
49
-7
128
1095
1380
50
-4.08
31.5
17.3
6.7
10.1
vineyard on clay
302
112
128
62
-3
59
1215
1572
50
-2.28
32.2
15.3
5.4
6.8
tigerbush
326
123
118
85
-5
79
1218
1639
50
-2.10
32.4
15.8
5.2
8.4
forest
310
117
97
96
-4
63
1125
1559
50
-1.74
32.2
15.3
5.1
8.1
Table VI.3: Values of analyzed parameters from the observations and calculated using the reference SVAT for the data simulation run
quantity
Q,D(dayl74)
HD (day 174)
XED (day 174)
GD (day 174)
HP (day 174)
XEtD (day 174)
z,12 (day 174)
z,M (day 174)
z,6 (day 175)
Am18 (day 174)
e„]s (day 174)
8„""" (day 175)
qW (day 174)
ami" (day 175)
units
W/m2
W/m2
W/m2
W/m2
W/m2
W/m2
m
m
m
mm
°C
°c
g/kg
g/kg
from observations
325
170
75
86
-16
126
2782
3185
72
-37.4
21.9
5.1
3.3
from reference SVAT
347
186
58
104
-11
139
2498
3187
55
-1.02
37.4
20.7
5.0
7.4
246 Sparse canopy parameterizations for meteorological models
Samenvatting
Modellen voor niet-gesloten vegetaties voor meteorologische toepassingen
• Probleemstelling en afbakening
Voor de voorspelling van het weer in de nabije toekomst, en het aardse klimaat in de
verdere toekomst, zijn grootschalige meteorologische modellen ontwikkeld. Deze
beschrijven voor de hele atmosfeer de huishouding van warmte, vocht, straling en andere
grootheden. Verschillende studies met weer- en klimaatmodellen hebben aangetoond dat de
resultaten gevoelig zijn voor de beschrijving van de uitwisseling van warmte, waterdamp en
impuls tussen de atmosfeer en het landoppervlak. Een verandering van bijvoorbeeld de
albedo, het bodemvochtgehalte, de aerodynamische ruwheid of de aanwezige vegetatie
levert grote veranderingen op in klimaatvoorspellingen. De toepassing van verschillende
landoppervlak-modellen is één van de redenen dat klimaatvoorspellingen onderling sterk
van elkaar kunnen verschillen. Het is duidelijk dat een realistische beschrijving van
landoppervlak-processen van belang is.
Minder duidelijk is hoe realistisch landoppervlak-modellen moeten zijn, en welke
mate van detail ze moeten bevatten. Erg gedetailleerde modellen geven wellicht
nauwkeuriger voorspellingen, maar zijn in de praktijk moeilijk toepasbaar vanwege de grote
hoeveelheid benodigde rekentijd en invoerinformatie. Er moet een keuze worden gemaakt
die een optimum biedt tussen complexiteit en nauwkeurigheid enerzijds, en eenvoud en
onnauwkeurigheid anderzijds.
Er zijn een groot aantal landoppervlak-modellen in omloop, ontwikkeld voor diverse
toepassingen, en met verschillende onderliggende fysische uitgangspunten. Voor gebruik
van een landoppervlak-model in grootschalige meteorologische toepassingen moet het een
groot aantal verschillende typen oppervlak kunnen beschrijven. Aanvankelijke waren alleen
modellen beschikbaar voor een relatief eenvoudig, homogeen oppervlak, maar in de loop
der jaren zijn verschillende modellen ontwikkeld die ook complexere typen oppervlak aan
kunnen. Tot zo'n type oppervlak behoort een vegetatie die de grond slechts gedeeltelijk
bedekt, een zogenaamd niet-gesloten gewas. Dit type vegetatie komt met name voor in semi-
aride, droge streken, waar water een beperkende factor is voor plantengroei. Modellen voor
niet-gesloten gewassen maken onderscheid tussen de planten en de onderliggende kale
grond. Voor elk van deze componenten wordt apart uitgerekend hoeveel warmte of
waterdamp wordt uitgewisseld met de atmosfeer.
Landoppervlak-modellen — en zeker die voor niet-gesloten vegetaties — beschrijven
een groot aantal processen. Ze beschouwen de hoeveelheid energie die het oppervlak
ontvangt in de vorm van straling, en berekenen de opwarming van de bodem en de lucht,
verdamping door planten en door de bodem, en de verandering van de vochttoestand van
de bodem. Al deze processen hangen met elkaar samen, en veranderingen aan een enkel
onderdeel van een model kunnen gevolgen hebben voor andere componenten. Doordat de
Samenvatting 2 4 7 •
verschillende modellen gebaseerd zijn op verschillende uitgangspunten zijn de voorspel
lingen verre van eenduidig. De vraag doet zich voor welke processen en grootheden het
warmte- en watertransport boven land het sterkst bepalen, en dus de meeste invloed hebben
op de toestand van de atmosfeer.
Bepalend voor deze keuze is de mate waarin de atmosfeer reageert op de
beschrijving van het landoppervlak. De onderste, turbulente laag van de atmosfeer (de
planetaire of atmosferische grenslaag, met een totale dikte van 0.5 à 3 km) heeft de
eigenschap om snel te reageren op veranderingen van het oppervlak. Tegelijkertijd worden
de transport-processen aan het oppervlak mede bepaald door de toestand van de atmosfeer.
Hierdoor ontstaat een terugkoppeling, die veranderingen kan versterken (positieve
terugkoppeling) of verzwakken (negatieve terugkoppeling). Hoe de atmosfeer reageert op
het landoppervlak wordt dus mede bepaald door deze terugkoppeling.
In dit proefschrift wordt een studie uitgevoerd waarin verschillende landoppervlak-
modellen met elkaar worden vergeleken, en gekeken wordt naar de veranderingen die de
atmosferische grenslaag ondervindt als gevolg van een verandering van de beschrijving van
het landoppervlak. Hierbij zijn een aantal accenten gelegd:
(1) Een eerste nadruk ligt op een beschouwing van uitwisselingsprocessen boven een niet-
gesloten vegetatie. Zo'n oppervlak heeft relatief uitgesproken eigenschappen op het
gebied van stralingshuishouding, aërodynamica en transport van warmte en
waterdamp. Op het moment dat deze studie begon was met name over de
modellering van niet-gesloten gewassen relatief weinig bekend. Dit type oppervlak
komt echter op grote schaal voor op aarde, en dit vormde een extra aanleiding om
ons met dit type oppervlak bezig te houden.
(2) De tweede nadruk ligt op de fysische benadering van uitwisselingsprocessen door de
diverse modellen. Er wordt gekeken naar de mate waarin de grenslaag reageert op
verschillende modellen die één enkel type oppervlak beschrijven, en niet op
verschillende oppervlakken die met één enkel model worden gesimuleerd.
(3) Nadruk nummer drie is de validatie van modellen door waarnemingen, die bij een niet-
gesloten gewas zijn verricht. Deze waarnemingen worden verder ook gebruikt om
modellen te ijken, en om als begintoestand en randvoorwaarde te dienen bij de
modelsimulaties.
(4) Tenslotte beschouwt deze studie alleen vertikale uitwisselingsprocessen. Simulaties worden
uitgevoerd met behulp van één-dimensionale modellen.
• De metingen
In twee zomers in 1991 en 1994 zijn metingen uitgevoerd bij een niet-gesloten
wijngaard in La Mancha, Spanje. De metingen vonden plaats in het kader van een groot
internationaal, deels door de EG gefinancierd project, genaamd EFEDA.
In Juni 1991 verrichtte de vakgroep Meteorologie van de Landbouwuniversiteit
Wageningen micrometeorologische waarnemingen in een uitgestrekte wijngaard nabij
Tomelloso, circa 100 km ten zuid-oosten van Madrid. Dit betrof metingen van straling,
luchttemperatuur en -vochtigheid, windsnelheid, en het transport van warmte en
waterdamp, zowel in de grond als in de lucht. Tegelijkertijd werd de aanwezige vegetatie
gedetailleerd in kaart gebracht: afmetingen, hoeveelheid bladoppervlak en met vegetatie
• 2 48 Sparse canopy parameterizations for meteorological models
bedekte grond, en het verdampingsgedrag van de planten zijn uitvoerig vastgelegd. Tijdens
de meetperiode werd het weer gekenmerkt door een vrijwel continue afwezigheid van
regen. De temperatuur van de (droge) lucht liep gemiddeld op tot circa 35 °C. Verder
groeide de vegetatie sterk. Hierdoor werd het terrein ruwer, en nam de verdamping
enigszins toe. De planten wortelden diep genoeg om water uit diepe grondlagen te
onttrekken. De bodem droogde langzaam maar zeker uit. Op het verdampingsgedrag van
de planten, en op de stralingseigenschappen van het oppervlak wordt later teruggekomen.
Gedurende deze campagne werden door collega's van het Franse Centre National de
Récherche Météorologique (CNRM) uit Toulouse metingen gedaan aan de toestand van de
atmosferische grenslaag, door middel van een temperatuur- en vochtsensor die aan een
stijgende ballon waren bevestigd. De gegevens van deze ballon-oplatingen zijn in dit
proefschrift gebruikt.
Tijdens de tweede meetcampagne werden metingen verricht over een langere
periode, Juni en Juli 1994. Deze meetcampagne was het resultaat van een intensieve
samenwerking met het Staring Centrum in Wageningen, en de Universiteit van
Kopenhagen. De vegetatiemetingen werden sterk geïntensiveerd, en ook is het transport van
C 0 2 gemeten. De waarnemingen werden op een soortgelijk veld gedaan als in 1991, maar de
planten waren wat jonger en hadden een kleinere hoeveelheid bladoppervlak. Het was nog
wat warmer en droger dan in 1991, en behalve de afwezigheid van regen werden er ook
nauwelijks wolken gesignaleerd gedurende de meeste dagen. Vooral de vegetatiemetingen
die in 1994 zijn verricht zijn voor deze studie gebruikt.
• Nadere beschouwing van een aantal uitwisselingsprocessen voor niet-gesloten
vegetaties Een aantal aspecten van de uitwisseling van warmte en waterdamp bij een niet-
gesloten gewas zijn nader bekeken, aan de hand van zowel theoretische analyse als van
metingen: aerodynamische uitwisseling, reflectie van kortgolvige straling, en de
zogenaamde gewasweerstand.
In eenvoudige meteorologische modellen wordt transport doorgaans beschreven aan
de hand van transportweerstanden. Deze zijn een maat voor de efficiëntie waarmee een
grootheid (bijvoorbeeld warmte) wordt getransporteerd over een gradient van die grootheid
(temperatuur). Meestal wordt verondersteld dat de fluxdichtheid (hoeveelheid getranspor
teerde grootheid per eenheid oppervlak per eenheid tijd) recht evenredig is met de lokale
gradient en een uitwisselingscoefficient. Deze theorie wordt aangeduid als K-theorie. In
sommige gevallen (zoals binnen gewassen) geldt de .K-theorie niet, en moeten meer
geavanceerde modellen worden gebruikt om de fluxdichtheid te beschrijven, zoals
bijvoorbeeld zogenaamde Lagrangiaanse modellen. Deze modellen berekenen het transport
van een grootheid door de trajectoriën van een groot aantal deeltjes te volgen, en nemen
derhalve veel rekentijd in beslag. In deze studie is een vereenvoudiging van een
Lagrangiaans model ontwikkeld voor toepassing in een twee-component landoppervlak
model, waaronder een model voor niet-gesloten gewassen. Een extra weerstand, een
zogenaamde near-field weerstand, is geïntroduceerd. Een gevoeligheidsanalyse toont aan, dat
onder de meeste omstandigheden het gebruik van K-theorie nauwelijks afwijkende
resultaten geeft ten opzichte van deze (vereenvoudigde) Lagrangiaanse theorie.
Samenvatting 249 *
Verder is de Lagrangiaanse theorie gebruikt om nieuwe transportweerstanden in een
twee-componenten-model te definieren, zonder — in tegenstelling tot de huidige praktijk —
aannames te doen over een effectieve bronhoogte. Met name voor niet-gesloten gewassen is
de aanname, dat de bron voor warmte en waterdamp zich op één enkele effectieve hoogte
bevindt, dubieus: waterdamp wordt vooral geëmitteerd door de aanwezige planten, terwijl
de bron voor warmte zich bevindt aan het oppervlak van de kale grond. In deze studie
wordt een wegingsprocedure voorgesteld die de transportweerstanden definieert als functie
van de vertikale verdeling van de bronnen. Opnieuw zijn gevoeligheidsstudies gedaan, en
zijn de nieuw verkregen weerstanden vergeleken met de waardes van traditionele modellen,
verkregen met JC-theorie. De voornaamste conclusies die hieruit voortkwamen zijn, dat de
'Lagrangiaanse' weerstanden over het algemeen kleiner zijn dan de traditionele weer
standen, en dat de verschillen met de K-theorie modellen aanzienlijk zijn. Dit laatste wordt
met name veroorzaakt door gebrek aan kennis over turbulentie vlak bij de grond.
De stralingswaarnemingen uit 1991 zijn gebruikt om de reflectie-eigenschappen van een
niet-gesloten gewas te beschrijven. Via een literatuur-onderzoek zijn de voornaamste aspecten
die de reflectie van kortgolvige straling (kortweg: albedo) bepalen op een rij gezet. Voor kale
grond wordt de albedo bepaald door de hoeveelheid bodemvocht in de bovenste laag, de
ruwheid van het oppervlak, het gehalte aan organisch materiaal en ijzer, en de stand van de
zon. Voor gesloten gewassen spelen met name de bladhoekverdeling, de hoeveelheid
bladoppervlak per eenheid grond-oppervlak (de Leaf Aera Index of LAI), de zonshoogte en
de reflectie-eigenschappen van de bladeren en de onderliggende grond een rol. Voor niet-
gesloten gewassen wordt de albedo door beide componenten bepaald, maar spelen ook
afstand tussen en afmetingen van de planten, en beschaduwing van de grond mee. Met
behulp van een aantal empirische vergelijkingen zijn de waarnemingen gefit. De dagelijkse
gang van de albedo vertoonde voornamelijk veranderingen bij lage zonshoogten. De
veranderingen over de hele maand werden veroorzaakt door twee tegenwerkende aspecten:
een verhoging van de albedo door uitdrogende grond, en een verlaging door toenemende
vegetatie. Hierdoor bleef voor een bepaalde positie de albedo redelijk gelijkmatig.
Bovendien zijn multi-spectrale satelliet-gegevens gebruikt om de horizontale spreiding van
de albedo in kaart te brengen. Het bleek dat deze horizontale spreiding veel groter was dan
de verandering in de tijd, zowel op een tijdschaal van een dag als die van de hele maand.
Een ander aspect dat in detail is bekeken is de zogenaamde gewasweerstand, een maat
voor de openingstoestand van de huidmondjes van planten. Een hoge weerstand correspon
deert met gesloten huidmondjes, en een lage evapotranspiratie. Met behulp van gegevens
uit 1991 heeft Jacobs (1994) een model voor de huidmondjesweerstand ontwikkeld dat
gebaseerd is op de modellering van de fotosynthese van planten. De fotosynthese
veroorzaakt een transport van C0 2 via diezelfde huidmondjes. Door dit transport te
beschrijven met een fotosynthese-model kan de huidmondjesweerstand afgeleid worden. In
dit proefschrift is dit model opgeschaald naar gewasniveau, en getest met behulp van 1994-
data. Het bleek dat de waarnemingen, opgeschaald naar gewasniveau, redelijk goed werden
beschreven met het door Jacobs (1994) ontwikkelde model, en ook dat de ijking die in 1991
was uitgevoerd goed bruikbaar was voor het nieuwe gewas. De prestaties van het model
lijken zelfs beter dan die van een veel toegepast model, dat gebaseerd is op een statistische
correlatie van de gewasweerstand met omgevingsfactoren. Vergelijking met soortgelijke
• 250 Sparse canopy parameterizations for meteorological models
waarnemingen uit de literatuur lieten zien dat de Spaanse wijnplanten een sterke
gevoeligheid voor de atmosferisch vochtigheid vertoonden, die waarschijnlijk gunstig is
onder droge omstandigheden.
• Modelsimulaties
De rest van dit proefschrift is gewijd aan modelsimulaties. Allereerst wordt een
beschrijving gegeven van de bestaande landoppervlak-modellen die in de vergelijkingen
zijn opgenomen. De eerste is het zogenaamde 'big leaf' model (Monteith, 1965), dat het land
oppervlak beschouwt als één enkel groot blad met een uniforme temperatuur en gewas
weerstand. Het tweede model is een variatie daarop, en beschouwt het landoppervlak als
een isotherme laag met daarin verschillende componenten: een fractie gevormd door kale
grond, een fractie vegetatie, en een fractie open water voor de beschrijving van dauw en
neerslag-interceptie (Viterbo en Beljaars, 1995; afgekort als VB95). Het derde model is een
nieuw ontwikkelde variant op het model van VB95. Het verschil met de oorspronkelijke
versie is dat voor elke fractie een aparte energiebalans wordt opgelost, waardoor de fracties
verschillende oppervlakte-temperaturen kunnen hebben. Deze variant is afzonderlijk getest
voor twee niet-gesloten gewassen waarin de temperaturen van het gewas en de kale grond
aanzienlijk kunnen verschillen. In de oude situatie werd de verdamping van de in
werkelijkheid koelste component sterk overschat door een te hoge temperatuur. In de
nieuwe situatie trad deze overschatting niet meer op. Het vierde model is het twee
component model van Deardorff (1978; hierna D78), waarin straling, aerodynamisch
transport en temperatuur van de kale grond en de vegetatie apart wordt beschouwd. Het
vijfde model is een variant op D78, maar heeft een meer geavanceerde beschrijving van de
aerodynamische uitwisseling binnen het gewas (Choudhury and Monteith, 1988; CM88).
Het gebruikte grenslaagmodel is dat van Troen en Mahrt (1986), waarin vertikaal
transport wordt beschreven met behulp van een numeriek diffusieschema. Voor convectieve
gevallen (overdag) zijn de diffusie-coefficienten ontleend aan Holtslag en Moeng (1991). Het
model geeft een redelijke beschrijving van de groei en opwarming van de grenslaag
overdag, het warmte- en vochttransport aan de top van de grenslaag, en de ontwikkeling
van een nachtelijke stabiele grenslaag.
• Modelsimulaties zonder grenslaageffecten Een eerste serie modelvergelijkingen werd uitgevoerd om het effect van de
verschillende fysische uitgangspunten in de diverse modellen op de gesimuleerde flux-
dichtheden van warmte en waterdamp te testen, en aan te geven welk model de observaties
van 1991 het beste beschreef. Hierbij werden alleen de twee component-modellen (VB95, D78
en CM88) betrokken, en grenslaageffecten werden nog niet meegenomen. Waarnemingen op
kleine hoogte (3 m) werden gebruikt als randvoorwaarde. Berekende fluxdichtheden van de
drie modellen werden vergeleken met waarnemingen. Uit deze vergelijking konden een
aantal duidelijke conclusies worden getrokken.
Ten eerste blijkt de simulatie van de bodemwarmtestroom niet goed te worden
uitgevoerd met een model dat de opslag van warmte in de bovenste bodemlaag negeert
(CM88). Een model dat de bodemwarmtestroom simuleert door de oplossing van een
diffusievergelijking (VB95) is vrij gevoelig voor de thermische eigenschappen die worden
Samenvatting 251 •
opgelegd. Een derde 'force-restore' variant, een vereenvoudiging van het diffusie-model (in
D78), bleek de beste resultaten op te leveren.
Een tweede belangrijke conclusie is dat de kwaliteit van de voorspellingen sterk
samenhangt met de beschrijving van de aerodynamische weerstand tussen waarnemings
hoogte en de kale grond-component van het oppervlak. Deze weerstand heeft een grote
invloed op de temperatuur van de kale grond, en die is weer maatgevend voor processen als
bodemverdamping, bodemwarmtestroom, opwarming van de lucht, en de temperatuur ter
hoogte van het gewas. De weerstanden zoals gemodelleerd in CM88 gaven de beste
resultaten, terwijl die in D78 veel te laag waren.
Vervolgens bleken de verschillende beschrijvingen van de gewasweerstand tot grote
verschillen in gesimuleerde verdamping te leiden. In zowel D78 als VB95 is die weerstand
sterk afhankelijk van de hoeveelheid bodemvocht, en deze afhankelijkheid leidde tot té
grote weerstanden en té lage verdampingen.
Opgemerkt moet worden dat het vaak moeilijk is om een 'eerlijke' vergelijking uit te
voeren. De modellen verschillen niet alleen in onderliggende theorie, maar ook in benodigde
invoer. Deze invoer moet uit veldwaarnemingen worden gehaald.
Uit deze vergelijking is een landoppervlakmodel geconstrueerd dat voor de huidige
dataset vermoedelijk de beste resultaten geeft. Het is een combinatie van de force-restore
methode ter beschrijving van de bodemwarmtestroom, en de aerodynamische weerstanden
en de gewasweerstand van CM88. Dit model dient als referentiemodel in de modelstudies
hieronder.
• Modelsimulaties met grenslaageffecten
Het laatste hoofdstuk van dit proefschrift beschrijft de modelsimulaties met behulp
van een groot aantal variaties van een landoppervlak-model, gekoppeld aan een model voor
de grenslaag. Het doel van deze simulaties was om na te gaan hoe de berekende toestand
van de grenslaag verandert ten gevolge van een wijziging van de modellering van de
landoppervlak-processen. Steeds werd voor een bepaalde simulatie eerst een modelrun
gedaan met behulp van het hierboven beschreven referentiemodel, de controlerun.
Vervolgens werden componenten van dit model vervangen door alternatieve componenten,
de simulatie opnieuw verricht, en werden de resultaten uitgedrukt in een relatieve
verandering ten opzichte van de controlerun. Dit uitwisselen van componenten werd
gedaan om de invloed van elke component apart te kunnen bekijken. Het vervangen van
complete modellen heeft als resultaat dat meerdere onderdelen in die modellen
verschillende (en mogelijk tegenstrijdige) gevolgen zouden kunnen hebben, en daardoor
interpretatie van de berekeningen zou bemoeilijken. De componenten die werden
uitgewisseld zijn ondergebracht in vier verschillende groepen:
(1) oppervlakte-representatie: hierin werd het twee-component model vergeleken met een 'big
leaf' aanpak, en met een al dan niet isotherme enkelvoudige oppervlaktelaag
(2) bodemwarmtestroom en bodemverdamping: hierin werd de force-restore methode vergeleken
met een diffusieschema, een weerstandsmodel, en een alternatieve beschrijving van
de bodemverdamping
(3) aerodynamische uitwisseling: hierin werden de weerstanden van CM88 vergeleken met die
in D78, en de weerstanden uit de Lagrangiaanse analyse
• 252 Sparse canopy parameterizations for meteorological models
(4) gewasweerstand: hierin werden verschillende modellen, waaronder het fotosynthese-
model, vergeleken.
De simulaties zijn uitgevoerd voor drie verschillende initialisaties: twee kunstmatige
profielen, en één situatie die in 1991 is gemeten. De kunstmatige profielen benaderen
zomerse omstandigheden in respectievelijk gematigde en Mediterrane streken. In alle
simulaties diende de Spaanse EFEDA-wijngaard als referentie-oppervlak. In een aantal
gevallen werden hierop (kleine) variaties aangebracht.
De computersimulaties zijn geëvalueerd aan de hand van daggemiddelde flux-
dichtheden van warmte, waterdamp en bodemwarmtestroom, fluxdichtheden van warmte
en waterdamp aan de top van de grenslaag, en de hoogte, temperatuur en vochtgehalte van
de grenslaag aan het eind van de middag en aan het eind van de daarop volgende nacht.
De volgende conclusies konden uit deze berekeningen worden getrokken:
(1) Voor de beschrijving van het warmte- en waterdamptransport boven een niet-gesloten
vegetatie is een twee-componenten model beter geschikt dan een 'big leaf' model, die
met name een forse overschatting van de verdamping veroorzaakt. Ook het onder
scheiden van verschillende fracties in een éénlagig model levert aanzienlijk betere
resultaten op.
(2) De beschrijving van de bodemwarmtestroom met een weerstandsschema zoals dat in
CM88 levert een forse onderschatting van deze grootheid, en daarmee een sterke
overschatting van het warmtetransport naar de atmosfeer. De force-restore methode
en het diffusiemodel leverden onderlinge verschillen van 30-40% in de
bodemwarmtestroom, en circa 20% in atmosferische warmte-fluxdichtheid. Deze
verschillen werden voornamelijk veroorzaakt door het verschil in thermische
geleiding, veroorzaakt door een verschil in berekend bodemvochtgehalte.
(3) De verschillende methoden om bodemverdamping te berekenen leidden tot aanzienlijke
verschillen in de totale verdamping. Deze verschillen waren sterk afhankelijk van het
bodemtype. De kwaliteit van alle gebruikte modellen berust sterk op empirische
grootheden, en is moeilijk objectief vast te stellen. Voor de droge bodem waarvoor de
simulaties zijn uitgevoerd lopen de modellen verder uiteen dan in vergelijkbare
studies onder minder extreme omstandigheden in de literatuur. Aan de andere kant
is onder droge omstandigheden de totale verdamping van geringe invloed op de
ontwikkeling van de grenslaag.
(4) De aërodynamische weerstanden zoals gesimuleerd in CM88 geven de beste beschrijving
van de oppervlaktetemperatuur en warmtefluxdichtheid.
(5) De in deze studie gesimuleerde warmtefluxdichtheid aan de top van de grenslaag (de
zogenaamde entrainment) is aanzienlijk lager dan uit diverse studies in de literatuur
bleek. Het feit dat de entrainment niet direkt is waargenomen maar uit de
computersimulaties is gehaald kan een reden voor dit verschil zijn. Vooral het feit
dat het effect van windschering op de entrainment in het gebruikte model niet is
meegenomen kan van belang zijn. Anderzijds kan de systematische aanwezigheid
van een duidelijke residulaag met een inversie op 3 km hoogte, de grenslaaggroei en
daarmee de entrainment in de huidige situatie hebben beperkt.
Samenvatting 253 •
Summary
Sparse canopy parameterizations for meteorological models
• Definition of the problem
For short-range weather prediction, and for predictions of the future global climate,
large-scale meteorological models have been developed. These models describe the budgets
of heat, moisture, radiation and other quantities for the entire atmosphere. Various studies
with weather- and climate models have shown that their results are sensitive to the
description of the exchange of heat, moisture and momentum between the land surface and
the atmosphere. Changes of for instance the surface albedo, the soil moisture content, the
aerodynamic roughness or the present vegetation can lead to major changes in climate
predictions. The application of different land surface models is one of the reasons for the
discrepancy between various climate predictions. It is clear that a realistic description of
land surface processes is of importance.
It is less obvious how realistic land surface models need to be, and what degree of
detail they must contain. Very detailed models may provide more accurate predictions, but
are hardly applicable in practice owing to the large demand of input information and
computer time. A choice must be made between complexity and accuracy on one hand, and
simplicity and inaccuracy on the other.
A large number of land surface models, developed for various applications and
containing different physical approaches, exists. For application in large scale meteorological
applications a large number of surface types must be described by the land surface scheme.
Early versions of these land surface models treated the surface as a relatively simple,
horizontally homogeneous surface, but in the past decades various models have been
developed that can also describe more complex surface types. Such a surface type is a
vegation only partially covering the ground, a so-called sparse canopy. This surface type is
typical for semi-arid, dry areas, where water is a limiting factor for vegetation growth.
Sparse canopy models distinguish between plants and the underlying bare ground. For each
of these components the exchange of heat and moisture with the atmosphere is calculated
separately.
Land surface models — and certainly those for sparse canopies — describe a large
number of processes. They consider the amount of energy received by the surface as
radiation, and compute the heating of the soil and the air near the surface, evaporation by
plants and soil, and the change of the soil moisture content. These processes are strongly
interrelated, and changes to a particular part of a model can result in major changes of other
components. Because of the different underlying physical concepts of the different models,
their results are far from uniform. The question arises, which processes and quantities most
strongly affect the transport of heat and moisture above the surface and the state of the
atmosphere.
• 2 5 4 Sparse canopy parameterizations for meteorological models
The response of the atmosphere to the description of the land surface is crucial for
this choice. The lowest, turbulent atmospheric layer (the planetary or atmospheric boundary
layer, 0.5 to 3 km deep), shows a quick response to changes of the land surface. Simul
taneously, transport processes near the surface are partially determined by the state of the
atmosphere. A feedback loop is formed, which can either increase (positive feedback) or
reduce (negative feedback) the effect of a land surface change. This feedback partially
determines the response of the atmosphere to the land surface description.
In this thesis a study is carried out in which various land surface schemes are
compared. The change of the atmospheric boundary layer as a result of a change of the
description of land surface processes is considered. Emphasis is put on the following issues:
(1) A first emphasis is that exchange processes for a sparse canopy vegetation type are
considered. This surface type has relatively extreme radiative and aerodynamic
properties, and the transport of heat and moisture takes place from various sources.
At the time this study was started, knowledge about sparse canopy models was
rather limited, in spite of the fact that sparse canopies are a very common global
surface type. This provided an additional reason to consider this surface type.
(2) The second emphasis is the physical approach of exchange processes in different land
surface models. The response of the planetary boundary layer to various models
describing a single surface type is investigated, rather than simulating different
surface types with a single model.
(3) Third, a model validation using observations taken at a sparsely vegetated site is carried out.
These observations were also used to calibrate models, and to serve as initial or
boundary conditions for the conducted model simulations.
(4) Finally, the study only considers vertical exchange processes. Simulations are carried out
with one-dimensional models.
• The measurements
In two summers in 1991 and 1994, measurements were carried out at a sparse canopy
vineyard site in La Mancha, Spain. The measurement campaigns took place in the context of
a large international project, partially sponsored by the EC, entitled EFEDA.
In June 1991 the Department of Meteorology of the Wageningen Agricultural
University carried out micrometeorological observations in a large vineyard near Tomelloso,
approximately 100 km south-east of Madrid. Measurements of radiation, air temperature
and -humidity, wind speed and transport of heat and moisture in both the ground and the
air were taken. Simultaneously the characteristic dimensions, leaf area and the surface
coverage of the present vegetation was monitored at various times during the period. Also
the vegetation evaporation properties were analysed. During the measurement campaign
the weather was characterized by an almost continuous absence of rain. The temperature of
the (dry) air typically reached values of 35 °C. Moreover, the vegetation showed a
significant growth. This caused an increase of the terrain roughness, and a small increase of
the evaporation. The plants had a sufficiently large rooting depth to extract water from deep
soil layers. The soil moisture content gradually decreased. In the following more attention is
paid to the radiation properties of the surface and the evaporation properties of the plants.
During the 1991 campaign colleagues of the Centre National de Récherche
Summary 255 •
Météorologique (CNRM) in Toulouse carried out radiosonde measurements, to monitor the
temperature, humidity and wind speed of the planetary boundary layer. The data from this
radiosoundings are used in the current study.
During the second held campaign in 1994, measurements were carried out over a
longer time span, June and July 1994. This measuring campaign was the result of an
intensive collaboration with the Wageningen Staring Centre and the university of
Copenhagen. The vegetation measurements were intensified, and also the vertical transport
of C 0 2 was measured. The observations were taken at a similar site as investigated in 1991,
but the plants were somewhat younger and had a smaller leaf area. The weather was
warmer than in 1991, and except for the absence of rain hardly any clouds were detected
during most days. Particularly the vegetation measurements were used for this study.
• A number of considered exchange processes
A number of aspects of the exchange of heat and moisture for a sparse canopy are
considered in more detail, using both theoretical analysis and measurements: aerodynamic
exchange, reflection of shortwave radiation, and the so-called crop resistance.
In applied meteorological models transport is usually described using exchange
resistances. These resistances are a measure of the efficieny of the transport of the quantity
(say, heat) over a gradient of a constituent (temperature). In most cases it is assumed that
the flux density (the amount of transported quantity per unit area per unit time) is propor
tional to the local gradient and an exchange coefficient. This theory is called K-theory. In
some cases (for instance, within canopies), K-theory is invalid, and sophisticated models
must be used to describe the flux density. One of this sophisticated theories is Lagrangian
theory, which describes the transport of a quantity by considering the trajectories of a large
number of released particles. This type of modelling is computationally very expensive. In
this study a simplification of a Lagrangian model has been developed for application in a
two-component land surface model, including a model for sparse canopies. A new
resistance, labeled a near-field resistance, is introduced. A sensitivity analysis shows that
under most circumstances the use of K-theory gives hardly different results compared to this
(simplified) Lagrangian theory.
This Lagrangian theory is also used to define new exchange resistances in a two-
component model, without — contrary to current practice — adopting assumptions about an
effective source height. Particularly for sparse canopies the assumption that sources of heat
and water vapour are situated at a similar effective height is doubtful: water vapour is
mainly released by the plants, while the heat source is mainly situated at the bare ground
surface. In the present study a weighing procedure, defining the exchange resistances as
function of the vertical distribution of sources, is proposed. Again sensitivity analyses are
carried out, and the newly obtained resistances are compared to the values of traditional
models obtained by JC-theory. The main conclusions are that the 'Lagrangian' resistances are
smaller than the traditional resistances, and that the differences with K-theory are
considerable. This feature is mainly caused by a lack of knowledge about the turbulence
close to the ground.
The 1991 radiation observations have been used to describe the reflection properties of
a sparse canopy. The most important aspects determining the reflection of shortwave
• 2 5 6 Sparse canopy parameterizations for meteorological models
radiation (albedo) were summarized from a literature survey. For bare soil the albedo is
determined by the soil moisture content in the very top soil layer, the surface roughness, the
content of organic material and iron, and the position of the sun. For closed canopies the leaf
angle distribution, the Leaf Area Index, the solar geometry and the reflection properties of
the individual leaves and underlying soil play a role. For sparse canopies the albedo is
determined by both components, but also by the distance between and dimensions of the
individual plants, and by shading of the soil. The observations were fitted using a set of
empirical relationships. The diurnal course of the albedo showed mainly changes at rather
low solar elevation. Changes over the entire month were caused by two counteracting
effects: an increase of the albedo by the drying of the soil, and a reduction by an increase of
the vegetation coverage. For a particular position the albedo was fairly constant. Also
multispectral satellite observations were used to detect the horizontal variability of the
surface albedo, which appeared to be much stronger than the changes in time, both on a
diurnal and a monthly time scale.
Another aspect that was considered in more detail is the so-called crop resistance, a
measure of the aperture of the leaf stomata. A high resistance corresponds to closed stomata
and low evaporation rates. Using the 1991 dataset, Jacobs (1994) developed a model for the
stomatal resistance based on leaf photosynthesis modelling. Photosynthesis results in a C0 2 -
transport through the same stomata. By describing this transport using a photosynthesis
model the stomatal resistance can be deduced. In the current thesis this model is scaled up
to the canopy level, and tested using the 1994 data. It appeared that the 1994 observations,
scaled up to the canopy level, were described fairly well by the model of Jacobs (1994), and
also that the calibration conducted in 1991 was still usable for the current dataset. The skill
of the model even seems to be better than the results of an often applied model, that is based
on a statistical correlation between the canopy conductance with environmental factors.
Comparisons with similar observations published in literature showed a strong sensitivity of
the Spanish vineplants to atmospheric humidity deficit. An enhanced humidity deficit is
likely to be favourable under very dry conditions.
• Model simulations
The remainder of the thesis is dedicated to model simulations. First a description is
given of the existing land surface models that are used in the intercomparison studies. The
first is a so-called 'big leaf' model (Monteith, 1965), that treats the surface as a single big leaf
with uniform temperature and canopy resistance. The second model is a variation upon this
scheme, and considers the land surface as a single isothermal layer with different
components: a fraction bare soil, a fraction vegetation, and a fraction open water
representing the dew and interception of precipitation (Viterbo and Beljaars, 1995;
abbreviated as VB95). The third model is a new variation on VB95, and solves the energy
balance for each surface fraction separately. This allows the different fractions to have
different surface temperatures. This variation is tested independently for two sparse canopy
surface types, in which the temperatures of the canopy and the underlying bare soil can be
very different. In the old situation the evaporation of the coolest component was
significantly overestimated by a too high surface temperature. In the new situation this
overestimation did not occur. The fourth model is the two-component scheme of Deardorff
Summary 257 •
(1978; hereafter referred to as D78), in which radiation, aerodynamic transfer and
temperature of the bare soil and the canopy elements are considered separately. The fifth
model is a variation of D78, but contains a more advanced description of the aerodynamic
exchange within the canopy layer (Choudhury and Monteith, 1988; CM88).
The model for the planetary boundary layer that was used is published by Troen and
Mahrt (1986). In that model the vertical transport is described using a numerical diffusion
scheme. For (daytime) convective cases the diffusion coefficients are taken from Holtslag
and Moeng (1991). The model gives a fair description of the growth and heating of the
planetary boundary layer during daytime, the heat and moisture transport near the top, and
the development of a nocturnal stable boundary layer.
• Model simulations without boundary layer effects
A first series of model comparisons was executed to test the effect of the different
physical approaches adopted in the various models upon the simulated flux densities of
heat and water vapour. It was also meant to indicate which model gave an optimal
description of the 1991 data. Only the two-component models (VB95, D78 and CM88) were
involved in this comparison, and boundary layer effects were not yet included. Observations
at a reference height of 3 m were used as boundary condition. Calculated flux densities were
compared to observations. A number of clear conclusions could be drawn from this
comparison study.
First, the simulation of the soil heat flux density was not carried out accurately with
a model ignoring the storage of heat in the upper soil layer (CM88). A model simulating the
soil heat flux density by solving a diffusion equation (VB95) appears to be rather sensitive for
the adopted soil thermal properties. A third 'force restore' variation, a simplification of the
diffusion model (in D78), yielded the best results.
A second conclusion is that the prediction quality is associated with the formulation
of the aerodynamic resistance between the reference height and the bare soil surface. This
resistance affects the the bare soil temperature, which has an impact on processes as soil
evaporation, soil heat flux density, sensible heat flux and the temperature within the canopy
air layer. The resistances as modelled in CM88 yielded optimal results, while those in D78
were too low.
The different descriptions of the canopy resistance lead to large relative differences
in predicted evaporation rate. In both D78 and VB95 this resistance is strongly determined by
the soil moisture content, and this dependence gave rise to too high resistances and too low
evaporation rates.
It must be noticed that it is often very difficult to perform an 'honest' model
comparison. The models differ in the underlying theory, and in required input data. This
input must be extracted from field observations.
The intercomparison was used to construct a land surface scheme that apparently
gives optimal predictions for the present dataset. It is a combination of the force-restore
method to describe the soil heat flux density, and the aerodynamic and canopy resistance
formulation in CM88. This model was used as a reference model for the model studies
described below.
258 Sparse canopy parameterizations for meteorological models
• Model simulations including boundary layer effects
The last chapter of this thesis describes model simulations using a large number of
variations to a land surface model, coupled to a model for the atmospheric boundary layer.
The purpose of these simulations is to investigate the sensitivity of the boundary layer to the
parameterization of land surface processes. For each case, first a model run was conducted
using the reference model described above, the control run. Then, components of this
reference model were changed by alternative components, and the simulations were
executed again. The results were expressed as relative differences compared to the control
run. Changing components rather than complete models was employed to be able to
describe the influence of each component separately. Changing complete land surface
schemes gives results which are difficult to interpret, since observed changes may have been
the result of multiple (and possibly counteracting) effects. The components that have been
exchanged are divided into four categories:
(1) surface representation: in this category the reference two-component model is compared to
a 'big leaf' approach, and to the isothermal and differentiated single layer surface
representations
(2) soil heat flux and soil evaporation: here the force-restore method is compared to a diffusion
scheme, a resistance model, and an alternative description of soil evaporation
(3) aerodynamic exchange: in this group the CM88 resistances were compared to the resistance
in D78, and to the resistances from the Lagrangian analysis
(4) canopy resistance: here different canopy resistance models, including the photosynthesis
approach, were compared.
The simulations have been executed for three different initializations: two artificial
profiles, and one situation measured in 1991. The artificial profiles resemble typical
summertime conditions in temperate and Mediterranean areas, respectively. In all
simulations the Spanish EFEDA vineyard served as reference surface. In a number of cases
small variations upon this surface were carried out.
The computer simulations have been evaluated by means of daily averaged flux
densities of sensible heat, water vapour and soil heat, sensible and latent heat flux densities
at the top of the boundary layer, and the boundary layer height, temperature and moisture
content near sunset and sunrise.
The following conclusions could be drawn from these calculations:
(1) For the description of the heat and moisture transport for a sparse canopy surface a two
component model is more suitable than a 'big leaf' approach, which particularly
computes a large overestimation of the surface evaporation. The differentiation
between various fractions of the single layer surface yields significantly better
results.
(2) The description of the soil heat flux density with a resistance scheme as in CM88 gives
rise to a pronounced underestimation of this quantity, associated with a strong
overestimation of the sensible heat transport into the atmosphere. The force restore
method and the diffusion scheme gave mutual differences of approximately 30 - 40%
in soil heat flux density, and 20% in sensible heat flux. These differences were mainly
Summary 259 •
caused by differences in thermal conductivity, resulting from differences in
calculated soil moisture content.
(3) The different methods to compute soil evaporation yielded considerable differences in
predicted total surface evaporation. These differences were strongly dependent on
the soil type. The quality of the models used relies on empirical quantities, and is
difficult to assess objectively. For the dry soil for which the simulations were carried
out, the models differed more than in comparable studies under less extreme
conditions reported in literature. On the other hand, the contribution of surface
evaporation to the atmospheric state is rather limited under the dry conditions
explored here.
(4) The aerodynamic resistance as simulated in CM88 resulted in an optimal description of
the surface temperature and sensible heat flux density.
(5) The sensible heat flux density at the top of the boundary layer simulated in this study
(the so-called heat entrainment) is very low compared to various experimental
studies in literature. In this study, entrainment was not observed but calculated,
which is one reason for this difference. Particularly the lack of simulating the
contribution of wind shear to entrainment may be of importance. Alternatively, the
systematic presence of a strong residual layer with an inversion at 3 km height has
confined the boundary layer growth, and thus the entrainment.
260 Sparse canopy parameterizations for meteorological models
Literature
Anonymous (1994): EFED.A CD-ROM Database: Vol. 1, Version 1, June 1994; European Communities, Directorate General XII for Science, Research and Development.
Baldocchi, D.D. (1992): A Lagrangian random-walk model for simulating water vapour, C 0 2 and sensible heat flux densities and scalar profiles over and within a soybean canopy; Boundary-Layer Meteorol. 61,113-144.
Baldocchi, D.D., B.B. Hicks and P. Camara (1987): A canopy stomatal conductance model for gaseous deposition to vegetated surfaces; Atmos.Environ. 21,91-101.
Ball, J.T. (1987): Calculations related to stomatal gas exchange; In: E. Zeiger, G.D. Farquhar and I.R. Cowan (Eds.), Stomatal Function; Stanford Univ. Press, Stanford, pp. 445-476.
Bastiaanssen, W.G.M. (1995): Regionalization of surface flux densities and moisture indicators in composite terrain: a remote sensing approach under clear skies in Mediterranean climates; PhD. thesis, Wageningen Agricultural University, 273 pp.
Bastiaanssen, W.G.M., D.H. Hoekman and R. A. Roebeling (1993): A methodology for the assessment of surface resistance and soil water storage variability at mesoscale based on remote sensing measurements (A case study with HAPEX-EFEDA data); Dept. of Hydrology, Wageningen Agricultural University, 71pp.
Begg, J.E., J.F. Bierhuizen, E.R. Lemon, D.K. Misra, R.O. Slatyer and W.R. Stern (1964): Diurnal energy and water exchanges in bulrush millet in an area of high solar radiation; Agric. Meteorol. 1,294-312.
Beljaars, A.C.M. (1992): Numerical schemes for parameterizations; ECMWF seminar proceedings, Sept. 1991; Numerical methods in atmospheric models, pp. 1-42.
Beljaars, A.C.M., P. Viterbo, M.J. Miller and A.K. Betts (1995): The anomalous rainfall over the USA during July 1993: sensitivity to land-surface parameterization and soil moisture anomalies; (accepted for publication by Monthly Weather Rev.).
Beljaars, A.C.M. and A.K. Betts (1992): Validation of the boundary layer scheme in the ECMWF model; ECMWF Seminar proceedings 7-11 September 1992; Validation of models over Europe, Vol. II, 159-195.
Beljaars, A.C.M. and A.A.M. Holtslag (1991): Flux parameterizations over land surface for atmospheric models; J.Appl.Meteorol. 30,327-341.
Bernstein, A.B. (1967): A note on the use of cup anemometers in wind profile experiments; J.Appl.Meteorol. 6, 280-286.
Betts, A.K. and J.H. Ball (1992): FIFE-1987 mean surface time series, Data diskette; Atmospheric Research, Pittsford, VT 05763.
Betts, A.K. and J.H. Ball (1994): Budget analysis of FIFE 1987 sonde data; J.Geophys.Res. 99D, 3655-3666. Bhumralkar, CM. (1975): Numerical experiments on the computation of ground surface temperature
in an atmospheric general circulation model; J.Appl.Meteorol. 14,1246-1258. Black, T.A., C.B. Tanner and W.R. Gardner (1970): Evaporation from a snap bean crop; Agronomy ƒ. 62,
66-69. Blondin, C. (1991): Parameterization of land-surface processes in numerical weather prediction; In:
T.J. Schmugge and J.C. André (Eds.), Land surface evaporation: measurements and parameterization; Springer, 31-54.
Blyth, E.M. (1995): Using a simple SVAT-scheme to describe the effect of scale on aggregation; Boundary-Layer Meteorol. 72, 267-285.
Blyth, E.M. and A.J. Dolman (1995): The roughness length for heat of sparse vegetation; J.Appl. Meteorol. 34, 583-585.
Blyth, E.M., A.J. Dolman and N. Wood (1993): Effective resistance to sensible- and latent-heat flux in heterogeneous terrain; Q.J.R.Meteorol.Soc. 119,423-442.
Bolle, H.J. and B. Streckenbach (1992): EFEDA - First annual report; Free University of Berlin, Germany, 259 pp. plus appendices.
Literature 261
Bolle, H.J. and B. Streckenbach (1993): The Echival Field Experiment in a Desertification Threatened Area -Final Report; Free Univ. of Berlin, Germany, 461 pp.
Bolle, HJ., J.C. André, J.L. Arme, H.K. Barth, P. Bessemoulin, A. Brasa, H.A.R. de Bruin, J. Cruces, G. Dugdale, ET. Engman, D.L. Evans, R. Fantechi, F. Fiedler, A. van de Griend, A.C. Imeson, A. Jochum, P. Kabat, T. Kratzsch, J.-P. Lagouarde, I. Langer, R. Llamas, E. Lopez-Baeza, J. Melia Miralies, L.S. Muniosguren, F. Nerry, J. Noilhan, H.R. Oliver, R. Roth, S.S. Saatchi, J. Sanchez Diaz, M. de Santa Olalla, W.J. Shuttleworth, H. Sogaard, H. Strieker, J. Thornes, M. Vauclin and D. Wickland (1993): EFEDA: European field experiment in a desertification threatened area; Ann.Geophysicae 11,173-189.
Bosilovich, M.G. and W.-Y. Sun (1995): Formulation and verification of a land surface parameterization for atmospheric models; Boundary-Layer Meteorol. 73, 321-341.
Braud, I., J. Noilhan, P. Bessemoulin, and P. Mascart (1993): Bare ground surface heat and water exchanges under dry conditions: observations and parameterization; Boundary-Layer Meteorol. 66,173-200.
Braud, I., A.C. Dantas-Antonino, M. Vauclin, J.L. Thony and P. Ruelle (1995): A simple soil-plant-atmosphere transfer model (SISPAT) development and field verification; J.Hydrol. 166,213-250.
Brown, K.W. and W. Covey (1966): The energy budget evaluation of the micro-meteorological transfer processes within a corn field; Agric.Meteorol. 3, 73-96.
Brutsaert, W. (1982): Evaporation into the atmosphere; D. Reidel Publ.Comp., Dordrecht, The Netherlands.
Brutsaert, W. (1986): Catchment-scale evaporation and the atmospheric boundary layer; Water Resources Res. 22, 39S-45S.
Buck, A.L. (1976): The variable path Lyman-alpha hygrometer and its operating characteristics; Bull.Am.Meteorol.Soc. 57,1113-1118.
Camillo, P.J. and R.J. Gurney (1986): A resistance parameter for bare soil evaporation models; Soil Sei. 141,95-105.
Campbell, G.S. (1977): An introduction to environmental biophysics; Springer-Verlag, New York, 159 pp. Charney, J.G., W.J. Quirk, S.H. Chow and J. Komfield (1977): A comparative study of the effects of
albedo change on drought in semi-arid regions; J.Atmos.Sci. 34,1366-1385. Choudhury, B.J. and J.L. Monteith (1986): Implications of stomatal response to saturation deficit for
the heat balance of vegetation; Agric.For.Meteorol. 36,215-225. Choudhury, B.J. and J.L. Monteith (1988): A four-layer model for the heat budget of homogeneous
land surfaces; Q.J.RMeteorol.Soc. 114,373-398. Choudhury, B.J., R.J. Regulato and S.B. Idso (1986): An analysis of infrared temperature observations
over wheat and calculation of latent heat flux; Agric.For.Meteorol. 37, 75-88. Clapp, R.B. and G.M. Hornberger (1978): Empirical equations for some hydraulic properties; Water
Resources Res. 14,601-604. Cionco, R.M. (1972): A wind profile index for canopy flow; Boundary-Layer Meteorol. 3, 255-263. Cionco, R.M. (1978): Analysis for canopy index values for various canopy densities; Boundary-Layer
Meteorol. 15,81-93. Collatz, G.J., M. Ribas-Carbo, and J.A. Ball (1992): Coupled photosynthesis-stomatal conductance
model for leaves of C4 plants; Aust.J.Plant Physiol. 19,519-538. Corrsin, S. (1974): Limitations of gradient transport models in random-walks and in turbulence; Adv.
Geophys. 18a, 25-60. Coulson, K.L. and D.W. Reynolds (1971): The spectral reflectance of natural surfaces; JAppl. Meteorol.
10,1285-1295. Covey, W. (1963): A method for the computation of the wind profile parameters and their standard
errors; Prod.Res.Rep. 72, Agric.Res.Serv., U.S.Agric.Dep., pp. 28-33. Cowan, I.R. (1968): Mass, heat and momentum exchange between stands of plants and their
atmospheric environment; Q.J.RMeteorol.Soc. 94,523-544. Cowan, I.R. (1982): Regulation of water use in relation to carbon gain in higher plants; In: O.L. Lange,
P.S. Nobel, C.B. Osmond and H. Ziegler (Eds.), Encyclopedia of Plant Physiology, New Series, Vol. 12B; Physiological Plant Ecology II, Springer Verlag, Berlin, pp 589-615.
Culf, A.D. (1992): An application of simple models to Sahelian convective boundary-layer growth; Boundary-Layer Meteorol. 58,1-18.
Daughtry, C.S.T. (1990): Direct measurements of canopy structure; Rem.Sens.Rev. 5,45-60. Deardorff, J.W. (1972): Theoretical expression for the countergradient vertical flux; J.Geophys.Res. 77,
5900-5904. Deardorff, J.W. (1978): Efficient prediction of ground surface temperature and moisture, with
inclusion of a layer of vegetation; J.Geophys.Res. 83,1889-1903.
• 262 Sparse canopy parameterizations for meteorological models
De Bruin, H.A.R. (1982): The energy balance of the Earth's surface: a practical approach; PhD-thesis, KNMI, De Bilt, The Netherlands.
De Bruin, H.A.R. (1983): A model for the Priestley-Taylor parameter a; J.Climate Appl. Meteorol. 22, 572-578.
De Bruin, H.A.R. (1987): Physical aspects of the planetary boundary layer with special reference to regional évapotranspiration; In: T.A. Black et al. (Eds.), Estimation ofareal évapotranspiration. Proceedings of an international workshop held during the Xixth General Assembly of the Int. Union of Geodesy and Geophysics at Vancouver, Canada, 9-22 Aug. 1987; IAHS Publ. no 177, IAHS Press, Wallingford, UK.
De Bruin, H.A.R., W. Kohsiek and B.J.J.M. van den Hurk (1993): A verification of some methods to determine the fluxes of momentum, sensible heat and water vapour using standard deviation and structure parameter of scalar meteorological quantities; Boundary-Layer Meteorol. 63, 231-257.
De Bruin, H.A.R., B.J.J.M. van den Hurk and W. Kohsiek (1995): The scintillation method tested over a dry vineyard area; (in press by Boundary-Layer Meteorol.)
Denmead, O.T. and E.F. Bradley (1985): Flux-gradient relationships in a forest canopy; In: B.A. Hutchison and B.B. Hicks (Eds.), The forest-atmosphere interaction; D. Reidel Publ., Dordrecht, pp. 421-441.
Dickinson, R.E. (1983): Land surface processes and climate - surface albedos and energy balance. Adv.Geoph. 25, 305-353.
Dickinson, R.E. (1988): The force-restore model for surface temperatures and its generalizations; J.Climate 1,1086-1097.
Dickinson, R.E., A. Henderson-Sellers, P.J. Kennedy and M.F. Wilson (1986): Biosphere-Atmosphere Transfer Scheme (BATS) for the NCAR Community Climate Model; NCAR Technical Note NCAR/TN-275+STR, 69 pp.
Dickinson, R.E. and A. Henderson-Sellers (1988): Modelling tropical deforestation: A study of GCM land surface parameterizations; QJ.R.Meteorol.Soc. 114,439-462.
Dickinson, R.E., A. Henderson-Sellers, C. Rosenzweig and P.J. Sellers (1991): Evapotranspiration models with canopy resistance for use in climate models: a review; Agric.t'or.Meteorol. 54, 373-388.
Dickinson, R.E., A. Henderson-Sellers and P.J. Kennedy (1993): Biosphere-Atmosphere Transfer Scheme (BATS) Version le as coupled to the NCAR Community Climate Model; NCAR Technical Note NCAR/TN-387+STR, 80 pp.
Dolman, A.J. (1993): A multiple source land surface energy balance model for use in GCMs; Agric.For.Meteorol. 65,21-45.
Dolman, A.J. and J.B. Stewart (1987): Modelling forest transpiration from climatological data; In: Swanson, Bernier and Woodard (Eds.), Forest Hydrology and Watershed Management; IAHS-publ. 167, pp. 319-327.
Dolman, A.J. and J.S. Wallace (1991): Lagrangian and K-theory approaches in modelling evaporation from sparse canopies; Q.J.R.Meteorol.Soc. 117,1325-1340.
Dolman, A.J., C.R. Lloyd and A.D. Culf (1992): Aerodynamic roughness of an area of natural open forest in the Sahel; Ann.Geophys. 10, 930-934.
Driedonks, A.G.M. (1981): Dynamics of the well-mixed atmospheric boundary layer; KNMl-report WR 81-2, KNMI, De Bilt, The Netherlands, 189 pp.
Driedonks, A.G.M. (1982a): Models and observations of the atmospheric boundary layer; Boundary-Layer Meteorol. 23,283-306.
Driedonks, A.G.M. (1982b): Sensitivity analysis for the equations for a convective mixed-layer; Boundary-Layer Meteorol. 22,475-480.
Droogers, P., G.D. van Abeele, J. Cobbaert, C.P. Kim, R. Rössleröva, M. Soet and J.N.M. Strieker (1993): Basic data sets description and preliminary results of EFEDA-Spain; Dept. of Water Resources, Wageningen Agricultural University, 103 pp.
Droppo, J.G. and H.L. Hamilton (1973): Experimental variability in the determination of the energy balance in a deciduous forest; J.Appl.Meteorol. 12, 781-791.
Dyer, A.J. and B.B. Hicks (1970): Flux-gradient relationships in the constant flux layer; Q.J.RMeteorol.Soc. 96, 715-721.
El-Kilani, R.M.M., A.F.G. Jacobs and J.H. van Boxel (1994): Intermittent canopy turbulent transport, correlations time domain maps and the resulting inherent inadequacy of using large time averaged second order closure to describe canopy turbulent transport processes; Proc. 21st Conf. on Agricultural and Forest Meteorology and 11th Conf. on Biometeorology and Aerobiology, March 7-11,1994, San Diego Calif., pp. 80-83.
263 i
Ellingson, R.G., J. Ellis and S. Fels (1991): The intercomparsion of radiation codes used in climate models: longwave results; J.Geoph.Res. 96,8929-8953.
Feddes, R.A. (1971): Water, heat and crop growth; Mededelingen Landbouwhogeschool 71-12, Wageningen, The Netherlands, 184 pp.
Friborg, Th. (1995): The use of carbon dioxide fluxes in climatology; PhD-thesis Copenhagen Unniversity, 67 pp.
Garratt, J.R. (1978): Transfer characteristics for a heterogeneous surface of large aerodynamic roughness; Q.J.R.Meteorol.Soc. 104,491-502.
Garrat, J.R. (1992): The atmospheric boundary layer; University Press, Cambridge, UK, 316 pp. Garrat, J.R. (1993): Sensitivity of climate simulations to land-surface and atmospheric boundary-layer
treatments - a review; f.Climate 6,419-449 Garratt, J.R. and B.B. Hicks (1973): Momentum, heat and water vapour transfer to and from natural
and artificial surfaces; Q.J.R.Meteorol.Soc. 99, 680-687. Gates, D.M. (1980): Biophysical Ecology; Springer Verlag, New York, 611 pp. Goudriaan, J. (1977): Crop micrometeorology: a simulation study; Wageningen Center for Agricultural
Publishing and Documentation, Wageningen, 249 pp. Goudriaan, J. (1988): The bare bones of leaf angle distribution in radiation models for canopy
photosynthesis and energy exchange; Agric.For.Meteorol. 43,155-170. Goudriaan, J. and H.H. van Laar (1978): Relations between leaf resistance, CCyconcentration and
C02-assimilation in maize, beans, lalang grass and sunflower; Photosynthetica 12, 241-249. Goudriaan, J., H.H. van Laar, H. van Keulen and W. Louwerse (1985): Photosynthesis, C 0 2 and plant
production; In: W. Day and R.K. Atkin (Eds.), Wheat growth and modelling; NATO ASI series, Series A, Vol. 86, Plenum Press, New York, 107-122.
Goutorbe, J.P., T. Lebel, A. Tinga, P. Bessemoulin, J. Brouwer, A.J. Dolman, J.H.C. Gash, M. Hoepffner, P. Kabat, Y.H. Kerr, B. Monteny, S. Prince, F. Said, P. Sellers and J. Wallace (1994): HAPEX-Sahel: a large scale study of land atmospheric interactions in the semi-arid tropics; Ann.Geophysicae 12, 53-64.
Graser, E.A. and C.H.M. van Bavel (1982): The effect of soil moisture upon soil albedo; Agric.Meteorol. 27,17-26.
Halldin, S. and A. Lindroth (1992): Errors in net radiometry. Comparison and evaluation of six radiometer designs; f.Atmos.Ocean.Techn. 9, 762-783.
Henderson-Sellers, A. and V. Gornitz (1984): Possible climatic impacts of land cover transformations, with particular emphasis on tropical deforestation; Clim.Change 6,231-258.
Henderson-Sellers, A. and V.B. Brown (1992): Project for Intercomparison of Land-surface Parameterization Schemes (PILPS); PILPS workshop report and first science plan; IGPO publication series No. 5, Science and Technology Corporation, Hampton, Virginia, USA, 32 pp. plus annexes.
Henderson-Sellers, A., Z.-L. Yang and R.E. Dickinson (1993): The project for intercomparison of land-surface parameterization schemes; Bull.Am.Meteorol.Soc. 74,1335-1349.
Henderson-Sellers, A., A.J. Pitman, P.K. Love, P. Irannejad and T.H. Chen (1995): The project for intercomparison of land-surface parameterization schemes (PILPS): phases 2 and 3; Bull.Am.Meteorol.Soc. 76,489-503.
Hicks, B.B. (1973): Eddy fluxes over a vineyard; Agric.Meteorol. 12,203-215. Hill, R.J., G.R. Ochs and J.J. Wilson (1992): Measuring surface-layer fluxes of heat and momentum
using optical scintillation; Boundary-Layer Meteorol. 58, 391-48. Hejstrup, J. (1981): A simple model for the adjustment of velocity spectra in unstable conditions
downstream of an abrubt change in roughness and heat flux; Boundary-Layer Meteorol. 21,341-356.
Holtslag, A.A.M. and A.P. van Ulden (1983): A simple scheme for daytime estimates of the surface fluxes from routine weather data; J.Clim. and Appl.Meteorol 22,517-529.
Holtslag, A.A.M. and C.-H. Moeng (1991): Eddy diffusivity and countergradient transport in the convective atmospheric boundary layer; J.Atmos.Sci. 48,1690-1698.
Holtslag, A.A.M. and F.T.M. Nieuwstadt (1986): Scaling the atmospheric boundary layer; Boundary-Layer Meteorol. 36,201-209.
Holtslag, A.A.M., E.I.F. de Bruijn and H.-L. Pan (1990): A high resolution air mass transformation model for short-range weather forecasting; Month.Wea.Rev. 118,1261-1575.
Holtslag, A.A.M., E. van Meygaard and W.C. de Rooy (1995): A comparison of boundary layer diffusion schemes in unstable conditions over land; (in press by Boundary-Layer Meteorol.).
Horton, R., P.J. Wierenga and D.R. Nielsen (1983): Evaluation of methods for determining the apparent thermal diffusivity of soil near the surface; Soi7.Sci.Soc./4m. 47,25-32.
• 264 Sparse canopy parameterizations for meteorological models
Huband, N.D.S. and J.L. Monteith (1986): Radiative surface temperature and energy balance of a wheat canopy. I: comparison of radiative and aerodynamic canopy temperature; Boundary-Layer Meteorol. 36,1-17.
Huntingford, C , S.J. Allen and R.J. Harding (1995): An intercomparison of single and dual-source vegetation-atmosphere transfer models applied to transpiration from Sahelian savannah; Boundary-Layer Meteorol. 74, 397-418.
Idso, S.B. (1981): A set of equations for full spectrum and 8- to 14-pm and 10.5- to 12.5-nm thermal radiation from cloudless skies; Water Resources Res. 17,295-304.
Idso, S.B., R.D. Jackson, R.J. Reginato, B.A. Kimball, and F.S. Nakayama (1975): The dependence of bare soil albedo on soil water content; J.Appl.Meteorol. 14,109-113.
Inclân, M.G. and R. Forkel (1995): Comparison of energy fluxes calculated with the Penman-Monteith equation and the vegetation models SIB and Cupid; J.Hydrol. 166,193-212.
Jacobs, A.F.G. and J.H. van Boxel (1988): Changes of the displacement height and roughness length of maize during a growing season; Agric.F'or.Meteorol. 42,53-62.
Jacobs, A.F.G. and W.A.J, van Pul (1990): Seasonal changes in the albedo of a maize crop during two seasons; Agric.For.Meteorol. 49, 351-360.
Jacobs, C.A. and P.S. Brown (1973): An investigation of the numerical properties of the surface heat-balance equation; J.Appl.Meteorol. 12,1069-1072.
Jacobs, C.M.J. (1994): Direct impact of atmospheric C02 enrichment on regional transpiration; PhD-thesis, Wageningen Agric. Univ., The Netherlands, 179 pp.
Jacobs, C.M.J, and H.A.R. de Bruin (1992): The sensitivity of regional transpiration to land-surface characteristics: significance of feedback; J.Climate 5,683-698.
Jacobs, C.M.J., B.J.J.M. van den Hurk and H.A.R. de Bruin (1995): Stomatal behavior and photosynthetic rate of unstressed grapevines in semi-arid conditions; (in press by Agric.For. Meteorol.)
Jarvis, P.G. (1976): The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field; Phil.Trans.R.Soc.London, Ser. B, 293,593-610.
Jarvis, P.G., G.B. James and J.J. Landsberg (1976): Coniferous forest; In: J.L. Monteith (Ed.), Vegetation and the atmosphere, Vol. 2, Academic Press, 171-240.
Kaimal, J.C., J.C. Wyngaard and D.A. Haugen (1968): Deriving power spectra from a three-component sonic anemometer; J.Appl.Meteorol. 7,827-834.
Kaimal, J .C, J.C. Wyngaard, Y. Izumi and O.R. Cote (1972): Spectral characteristics of surface layer turbulence; Q.J.R.Meteorol.Soc. 98,563-589.
Kawatani, T. and R.N. Meroney (1970): Turbulence and wind speed characteristic within a model canopy flow field; Agric.Meteorol. 7,143-158.
Kelliher, F.M., R. Leuning, M.R. Raupach and E.-D. Schulze (1995): Maximum conductances for evaporation from global vegetation types; Agric.For.Meteorol. 73,1-16.
Keijman, J.Q. (1974): The estimation of the energy balance of a lake from simple weather data; Boundary-Layer Meteorol. 7,399-407.
Kim, J. and S.B. Verma (1991a): Modeling canopy photosynthesis: scaling up from a leaf to canopy in a temperate grassland ecosystem; Agric.For.Meteorol. 57,187-208.
Kim, J. and S.B. Verma (1991b): Modelling canopy stomatal conductance in a temperate grassland ecosystem; Agric.For.Meteorol. 55,149-166.
KNMI (1981): Codevorm en codes voor de SYNOP en de KLIM; KNMI, The Netherlands, 168 pp. (in Dutch)
Kohsiek, W. (1982): Measuring CT , CQ and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture; Boundary-Layer Meteorol. 24, 89-107.
Kohsiek, W., H.A.R. de Bruin, H. The and B. van den Hurk (1993): Estimation of the sensible heat flux of a semi-arid area using surface radiative temperature measurements; Boundary-Layer Meteorol. 63,213-230. (See also: Kohsiek et al, 1994)
Kohsiek, W., H.A.R. de Bruin, H. The and B. van den Hurk (1994): Corrigendum to 'Estimation of the sensible heat flux of a semi-arid area using surface radiative temperature measurements'; Boundary-Layer Meteorol. 69, 215-217.
Kondo, J., N. Saigusa and T. Sato (1990): A parameterization of evaporation from bare soil surfaces; J.Appl.Meteorol. 29,385-389.
Kondo, J., N. Saigusa and T. Sato (1992): A model and experimental study of evaporation from bare-soil surfaces; J.Appl.Meteorol. 31, 304-312
Koracin, D. and R. Berkowicz (1988): Nocturnal boundary-layer height: observations by acoustic sounders and predictions in terms of surface-layer parameters; Boundary-Layer Meteorol. 43, 65-83.
Literature 265 •
Koster, R. and M. Suarez (1992): Modelling the land surface boundary in climate models as a composite of independent vegetation stands; J.Geophys.Res. 97,2697-2715.
Krikke, R.H. (1994a): Quicksel Manual; Dept. of Meteorology, Wageningen Agricultural University, 19 pp.
Krikke, R.K. (1994b): Comparison ofdetrended variance calculation methods; Dept. Of Meteorology, Agricultural University, Wageningen.
Kustas, W.P., B.J. Choudhury, M.S. Moran, R.J. Reginato, R.D. Jackson, L.W. Gay and H.L. Weaver (1989): Determination of sensible heat flux over sparse canopy using thermal infrared data; Agric.For.Meteorol. 44,197-216.
Legg, B.J. and M.R. Raupach (1982): Markov-chain simulation of particle dispersion in inhomogeneous flows: the mean drift velocity induced by a gradient in Eulerian velocity variance; Boundary-layer Meteorol. 24,3-13.
Lenschow, D.H., J.C. Wyngaard and W.T. Pendell (1980): Mean-field and second-moment budgets in a baroclinic, convective boundary layer; J.Atmos.Sci. 37,1313-1326.
Leuning, R. and J.B. Moncreiff (1990): Eddy-covariance C 0 2 flux measurements using open- and closed-path C 0 2 analysers: corrections for analyser water vapour sensitivity and damping of fluctuations in air sampling tubes; Boundary-Layer Meteorol. 53, 63-76.
Leuning, R. and K.M. King (1992): Comparison of eddy-covariance measurements of C 0 2 fluxes by open- and closed-path C 0 2 analysers; Boundary-Layer Meteorol. 59,297-311.
Lloyd, CR., J.H.C. Gash and M.V.K. Sivakumar (1992): Derivation of the aerodynamic roughness parameters for a Sahelian savannah site using the eddy correlation technique; Boundary-Layer Meteorol. 58,261-271.
Louis, J.-F. (1979): A parametric model of vertical eddy fluxes in the atmosphere; Boundary-Layer Meteorol. 17,187-202.
Mahfouf, J.F. and J. Noilhan (1991): Comparative study of various formulations of evaporation from bare soil using in situ data; J.Appl.Meteorol. 30,1354-1365.
Mahrt, L. and H.-L. Pan (1984): A two-layer model for soil hydrology; Boundary-Layer Meteorol. 29 ,1-20.
Malhi, Y.S. and B.J.J.M. van den Hurk (1992): Net radiometer comparison experiments during the EFEDA-campaign; In: H.J. Bolle and B. Streckenbach (Eds.), EFEDA -first annual report; Univ. of Berlin, 241-254.
Manabe, S. (1969): The atmospheric circulation and hydrology of the Earth's surface; Mon.Weather Rev. 97, 739-774.
Mayocchi, C.L. and K.L. Bristow (1995): Soil surface heat flux: some general questions and comments on measurements; Agric.For.Meteorol. 75,43-50.
McArthur, A.J. (1990): An accurate solution to the Penman equation; Agric.For.Meteorol. 51,87-92. McBean, G.A. (1972): Instrument requirements for eddy correlation measurements; J.Appl.Meteorol. 11,
1078-1084. McClatchey, R.A., R.W. Fenn, J.E.A. Selby, F.E. Volz and J.S. Garing (1971): Optical properties of the
atmosphere; Rep. Air Force Cambridge Res.Lab.-71-0279, Bedford, Massachussets, 85 pp. Mcintosh, D.H. and A.S. Thorn (1983): Essentials of meteorology; Taylor & Francis Ltd, London, 238 pp . McMillen, R.T. (1988): An eddy-correlation technique with extended applicability to non-simple
terrain; Boundary-Layer Meteorol. 43,231-245. McNaughton, K.G. and P.G. Jarvis (1983): Predicting effects of vegetation changes on transpiration
and evaporation. In: T.T. Kozlowski (Ed.), Water deficits and plant growth, Vol. 7, Academic Press, New York, pp. 1-47.
McNaughton, K.G. and T.W. Spriggs (1986): A mixed layer model for regional evaporation; Boundary-Layer Meteorol. 34, 243-262.
McNaughton, K.G. and B.J.J.M. van den Hurk (1995): A 'Lagrangian' revision of the resistors in the two-layer model for calculating the energy budget of a plant canopy; Boundary-Layer Meteorol. 74,261-288.
Menenti, M., W.G.M. Bastiaanssen and D. van Eick (1989): Determination of surface hemispherical reflectance with Thematic Mapper data; Remote Sensing Environ. 28, 327-337.
Meyers, T.P. and K.T. Paw U (1986): Testing of a higher-order closure model for modelling airflow within and above plant-canopies; Boundary-Layer Meteorol. 37, 297-311.
Meyers, T.P. and K.T. Paw U (1987): Modelling the plant canopy micrometeorology with higher-order closure principles. Agric.For.Meteorol. 41,143-163.
Michels, B.I. and A.F. Moene (1991): The contribution of the Department of Meteorology, WAU, to the EFEDA pilot study: project performance and results on crop development and roughness parameters; Dept. of Meteorology, Wageningen Agricultural University, 78 pp.
• 266 Sparse canopy parameterizations for meteorological models
Michels, B.I. and A.M. Jochum (1995): Heat and moisture flux profiles in a region with inhomogeneous surface evaporation; J.Hydrol. 166,383-408.
Milly, P.C.D. and K.A. Dunne (1994): Sensitivity of the global water cycle to the water-holding capacity of land; J.Climate 7,506-526.
Mintz, Y. (1984): The sensitivity of numerically simulated climates to land surface boundary conditions. In: J.T. Houghton (Ed.), The Global Climate, Cambridge University Press, pp. 79-105.
Moene, A.F., H.A.R. De Bruin and A.A.M. Holtslag (1995): Validation of the surface parametrization of HIRLAM using surface-based measurements and remote sensing data; KNMI Scientific report WR 95-07, 45 pp.
Moene, A.F. (1992): Intercomparison of energy fluxes measured during EFEDA; Dept. of Meteorology, Wageningen Agricultural University, Wageningen, The Netherlands, 33 pp.
Moeng, C.-H. and J.C. Wyngaard (1984): Statistics of conservative scalars in the convective boundary layer; J.Atmos.Sci 41,3161-3169.
Moeng, C.-H. and J.C. Wyngaard (1989): Evaluation of turbulent transport and dissipation closures in second-order modeling; J.Atmos.Sci. 46,2311-2330.
Moncreiff, J.B., J.M. Massheder, H.A.R. De Bruin, J. Eibers, T. Friborg, B.G. Heusinkveld, P. Kabat, S. Scott, H. Sogaard and A. Verhoef (1995): A system to measure surface fluxes of momentum, sensible heat flux, water vapour and carbon dioxide; (Accepted for publication by J.Hydrol.)
Monna, W.A.A., W. Kohsiek, G.J. Prangsma, J.N. Roozekrans and J.G. van der Vliet (1994): EFEDA-91 Documentation of measurements obtained by KNMI; Techn.Rep. TR-171, KNMI, De Bilt, The Netherlands, 13 pp.
Monteith, J.L. (1965): Evaporation and the environment; Symp.Soc.Exp.Biol. 19,205-234. Monteith, J.L. (1973): Principles of environmental physics; Edward Arnold Press, London. Monteith, J.L. (1981): Evaporation and surface temperature; Q.J.R.Meteorol.Soc. 107,1-27. Monteith, J.L. (1993): The exchange of water and carbon by crops in a mediterranean climate. Irrig.
Sei. 14, 85-91. Monteith, J.L. (1995a): Accomodation between transpiring vegetation and the convective boundary
layer; J.Hydrol. 166, 251-264. Monteith, J.L. (1995b): A reinterpretation of stomatal responses to humidity; Plant, Cell and
Environment 18, 357-364. Monteith, J.L., G.S. Campbell and E.A. Potter (1988): Theory and performance of a dynamic diffusion
porometer; Agric.For.Meteorol. 44, 27-38. Moore, C.J. (1986): Frequency response corrections for eddy correlation systems; Boundary-Layer
Meteorol. 37,17-35. Morison, J.I.L. and R.M. Gifford (1983): Stomatal sensitivity to carbon dioxide and humidity: a
comparison of two C3 and two C4 grass species; Plant Physiology 71, 789-796. Mott, K.A. and D.F. Parkhurst (1991): Stomatal response to humidity in air and helox. Plant, Cell and
Environment 14, 509-515. Myers, V.l. and W.A. Allen (1968): Electro-optical remote sensing methods as nondestructive testing
and measuring techniques in agriculture; Applied optics 7,1819-1838. Noilhan, J. and S. Planton (1989): A simple parameterization of land surface processes for
meteorological models; Mon.Weather Rev. 117,536-549. Norman, J.M. (1982): Simulation of microclimates; In: J.L. Hatfield and I.J. Thompson (Eds.),
Biometeorology in integrated pest management; Academic Press, New York, pp. 205-234. Norman, J.M. and J.M. Welles (1983): Radiative transfer in an array of canopies; Agronomy J. 75,481-
488. Oke, T.R (1978): Boundary layer climates; Methuen & Co Ltd, London, UK, 372 pp. Panofsky, H.A., H. Tennekes, D.H. Lenschow and J.C. Wyngaard (1977): The characteristics of
turbulent velocity components in the surface layer under convective conditions; Boundary-Layer Meteorol. 11,355-361.
Panofsky, H.A. and J.A. Dutton (1984): Atmospheric turbulence; models and methods for engineering applications; Wiley and Sons, New York
Paulson, C.A. (1970): The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer; J.Appl.Meteorol. 9, 857-861.
Pereira, A.R. and R.H. Shaw (1980): A numerical experiment on the mean wind structure inside canopies of vegetation; Agric.For.Meteorol. 22,303-318.
Philip, J.R. (1957): Evaporation, and moisture and heat fields in the soil; J.Meteorol. 14, 354-366. Philip, J.R. (1961): The theory of heat flux meters; J.Geophys.Res. 66,571-579. Philip, J.R. (1963): The damping of a fluctuating concentration by continuous sampling through a
tube; Aust.J.Phyj. 16,454-463.
Literature 267 •
Press, W.H., B.P Flannery, S.A. Teukolsky and W.T. Vetterling (1986): Numerical Recipes; Cambridge University Press, Cambridge, 818 pp.
Priestley, C.H.B, and R.J. Taylor (1972): On the assessment of surface heat flux and evaporation using large-scale parameters; Mon.Weather Rev. 100,81-92.
Raupach, MR. (1988): Canopy Transport Processes; In: W.L. Steffen and O.T. Denmead (Eds.), Flow and Transport in the Natural Environment: Advances and Applications; Springer-Verlag, Berlin, pp. 95-127.
Raupach, M.R. (1989a): A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies; Q.J.RMeteorol.Soc. 115,609-632.
Raupach, M.R. (1989b): Applying Lagrangian fluid mechanics to infer scalar source distributions from concentration profiles in plant canopies; Agric.For.Meteorol. 47,85-108.
Raupach, M.R. (1991): Vegetation-atmosphere interaction in homogeneous and heterogeneous terrain: some implications of mixed-layer dynamics; Vegetatio 91,105-120.
Raupach, M.R. (1992): Drag and drag partition on rough surfaces; Boundary-Layer Meteorol. 60, 375-395.
Raupach, M.R. and J.J. Finnigan (1988): 'Single layer models of evaporation from plant canopies are incorrect but useful, whereas multilayer models are correct but useless': discuss; Aust.J.Plant.Physiol. 15, 705-716.
Raupach, M.R. and A.S. Thom (1981): Turbulence in and above plant canopies; Ann.Rev.Fluid.Mech. 13, 97-129.
Robinson, S.M. (1962): Computing wind profile parameters; J.Atmos.Sci. 19,189-190. Rowntree, P.R. (1991): Atmospheric parameterization schemes for evaporation over land: basic
concepts and climate modeling aspects; In: Schmugge and André (Eds.), Land Surface Evaporation; Measurement and Parameterization; Springer-Verlag, New York, pp. 5-30.
Rowntree, P.R. and A.B. Sangster (1986): Remote Sensing needs identified in climate model experiments with hydrological and albedo changes in the Sahel; Proc. ISLSCP Conference, Rome, ESA SP-248, pp. 175-183.
Sato, N., P.J. Sellers, D.A. Randall, E.K. Schneider, J. Shukla, J.L. Kinter III, Y-T. Hou and E. Albertazzi (1989): Effects of implementing the Simple Biosphere model in a General Circulation Model; J.Atmos.Sci. 18,2757-2782.
Sawford, B.L. (1986): Generalized random forcing in random-walk turbulent dispersion models; Phys.Fluids 29, 3582-3585.
Schmugge, T.J. and J.C. André (Eds.) (1991): Measurement and parameterization of land surface evaporation fluxes; Springer Verlag, New York.
Schotanus, P., F.T.M. Nieuwstadt and H.A.R. de Bruin (1983): Temperature measurement with a sonic anemometer and its applications to heat and moisture fluxes; Boundary-Layer Meteorol. 26, 81-93.
Sellers, P.J. (1985): Canopy reflectance, photosynthesis and transpiration; Int.J.Remote Sensing 6,1335-1372.
Sellers, P.J., Y. Mintz, Y.C. Sud and A. Dalcher (1986): A simple biosphere model (SiB) for use within general circulation models; J.Atmos.Sci. 43,505-531.
Sellers, P.J., F.G. Hall, G. Asrar, D.E. Strebel and R.E. Murphy (1988): The first ISLSCP field experiment (FIFE); Bull.Am.Meteorol.Soc. 69, 22-27.
Sene, K.J. (1994): Parameterisations for energy transfers from a sparse vine crop; Agric.For.Meteorol. 71,1-18.
Shao, Y., R.D. Anne, A. Henderson-Sellers, P. Irannejad, P. Thornton, X. Liang, T.H. Chen, C. Ciret, C. Desboroough, O. Balachova, A. Haxeltine and A. Ducharne (1994): Soil moisture simulation: a report of the RICE and PILPS workshop; Clim.Impacts Centre, IGPO Publ. Seri. No. 14,179 pp.
Shaw, R.H. and A.R. Pereira (1982): Aerodynamic roughness of a plant canopy: a numerical experiment; Agric.Meteorol. 26, 51-65.
Shiozawa, S. and G.S. Campbell (1990): Soil thermal conductivity; Rem.Sens.Rev. 5, 301-310. Shukla, J. and Y. Mintz (1982): Influence of land surface évapotranspiration on the Earth's climate;
Science 215,1498-1501. Shuttleworth, W.J (1988): Macrohydrology - the new challenge for process hydrology; J.Hydrol. 100,
31-56. Shuttleworth, W.J. and J.S. Wallace (1985): Evaporation from sparse crops - an energy combination
theory; Q.J.RMeteorol.Soc. I l l , 839-855. Shuttleworth, W.J. and R.J. Gurney (1990): The theoretical relationship between foliage temperature
and canopy resistance in sparse crops; Q.J.RMeteorol.Soc. 116,497-519.
2 6 8 Sparse canopy parameterizations for meteorological models
Shuttleworth, W.J., J.H.C. Gash, CR. Lloyd, D.D. McNeil, C.J. Moore and J.S. Wallace (1988): An integrated micrometeorological system for evaporation measurement; Agric.For.Meteorol. 43, 295-317.
Sinclair, T.R., L.H. Allen and E.R. Lemon (1975): An analysis of errors in the calculation of energy flux densities above vegetation by a Bowen-ratio profile method; Boundary-Layer Meteorol. 8,129-139.
Slater, P.N. (1980): Remote-sensing optics and optical systems; Addison-Wesley Publ.Comp., Reading, UK, 575 pp.
Stewart, J.B. (1988): Modelling surface conductance of pine forest; Agric.For.Meteorol. 43,19-35. Stull, R.B. (1988): An introduction to Boundary Layer Meteorology; Kluwer Academic Publ., Dordrecht,
The Netherlands, 666 pp. Sud, Y.C., P.J. Sellers, Y. Mintz, M.D. Chou, G.K. Walker and W.E. Smith (1990): Influence of the
biosphere on the global circulation and hydrological cycle - a GCM simulation experiment; Agric.For.Meteorol. 52,133-180.
Taylor, G.I. (1959): The present position in the theory of turbulent diffusion; Adv.Geophys. 6,101-112. Ten Berge, H.F.M. (1990): Heat and water transfer in bare topsoil and the lower atmosphere; PUDOC,
Wageningen, The Netherlands, 207 pp. Tennekes, H. (1973): A model for the dynamics of the inversion above a convective boundary layer;
J.Atmos.Sci. 30, 558-567. Tennekes, H. and J.L. Lumley (1972): A first course in turbulence; MIT Press, Massachusetts, 300 pp. Thorn, A.S. (1972): Momentum, mass and heat exchange of vegetation; Q.J.R.Meteorol.Soc. 98,124-134. Thorn, A.S. (1975): Momentum, mass and heat exchange of plant communities. In: J.L. Monteith (Ed.),
Vegetation and the Atmosphere, Vol. 1: Principles; Academic Press, Orlando, USA, pp. 57-109. Tillman, J.E. (1991): In situ water vapor measurements in the Lyman-alpha and infrared spectrum:
theory and components; In: Schmugge and André (Eds.), Land Surface Evaporation; Measurement and Parameterization; Springer-Verlag, New York, pp. 313-335.
Troen, I. and L. Mahrt (1986): A simple model of the atmospheric boundary layer; sensitivity to surface evaporation; Boundary-Layer Meteorol. 37,129-148.
Turner, N.C. (1991): Measurement and influence of environmental and plant factors on stomatal conductance in the field; Agric.For.Meteorol. 54,137-154.
Van Asselt, C.J., A.F.G. Jacobs, J.H. van Boxel and A.E. Jansen (1991): A rigid fast-response thermometer for atmospheric research; Meas.Sci.Technol. 2, 26-31.
Van de Griend, A.A. and M. Owe (1994): Bare soil surface resistance to evaporation by vapor diffusion under semi-arid conditions; Water Resources Res. 30,181-188.
Van de Griend, A.A., M. Owe, H. Vugts and S.D. Prince (1989): Water and surface energy balance modeling in Botswana; Bull.Am.Meteorol.Soc. 70,1404-1411.
Van den Hurk, B.J.J.M. (1995): The influence of the detrending algorithm on computed eddy-correlation covariance; Dept. of Meteorology, Agricultural University, Wageningen.
Van den Hurk, B.J.J.M. and D.D. Baldocchi (1990): Random-walk models for simulating water vapor exchange within and above a soybean canopy; NOAA Technical Memorandum ERL ARL-185, NOAA, Air Resources Laboratory, Silver Springs, Maryland, 46 pp.
Van den Hurk, B.J.J.M. and A.C.M. Beljaars (1995): Impact of some simplifying assumptions of the new ECMWF surface scheme; (submitted for publication to J.Appl.Meteorol.)
Van den Hurk, B.J.J.M. and H.A.R. de Bruin (1993): Surface fluxes measured during EFEDA; In: Bolle, H.J. and B. Streckenbach (Eds.), The ECHIVAL Field Experiment in a Desertification-threatened Area (EFEDA) - Final report, Univ. of Berlin, pp. 141-227.
Van den Hurk, B.J.J.M. and H.A.R. de Bruin (1995): Fluctuations of the horizontal wind under unstable conditions; Boundary-Layer Meteorol. 74, 341-352.
Van den Hurk, B.J.J.M. and K.G. McNaughton (1995): Implementation of near-field dispersion in a simple two-layer surface resistance model; J.Hydrol. 166,293-311.
Van den Hurk, B.J.J.M., A. Verhoef, A.R. van den Berg and H.A.R. de Bruin (1995): An intercomparison of three vegetation/soil models for a sparse vineyard canopy; (In press by Q.J.R. Meteorol.Soc.)
Van Haneghem, I.A. (1981): Een niet-stationaire naaldmethode (warmtegeleiding, warmtecapaciteit, contactweerstand); PhD-thesis, Dept. of Physics, Wageningen Agricultural University, The Netherlands, 187 pp.
Van Heemst (1986): Potential crop production. In: H. van Keulen & J. Wolf (Eds.), Modelling of agricultural production: weather, soil and crops. Simulation Monographs, Pudoc, Wageningen.
Van Wijk, W.R. (1963): Physics of plant environment; North Holland Publishers, Amsterdam, 382 pp. Verhoef, A. (1995): Surface energy balance of shrub vegetation in the Sahel; PhD-thesis, Dept. of
Meteorology, Wageningen Agricultural University, 247 pp.
Literature 269 •
Verhoef, A., B.J.J.M. van den Hurk, A.F.G. Jacobs and B.G. Heusinkveld (1995): Thermal soil properties for a vineyard (EFEDA-I) and a savanna (HAPEX-Sahel) site; (in press by Agric.For. Meteoroh).
Viterbo, P. and A.C.M. Beljaars (1995): An improved land surface parameterization scheme in the ECMWF-model and its validation; Technical Report TR 75, ECMWF, Reading, 52 pp. (also accepted for publication by ƒ. Climate)
Waggoner, P.E. and W.E. Reifsnyder (1968): Simulation of the temperature, humidity and evaporation profiles in a leaf canopy. J.Appl.Meteorol. 7,400-409.
Wallace, J.S., J.M. Roberts and M.V.K. Sivakumar (1990): The estimation of transpiration from sparse dryland millet using stoma tal conductance and vegetarian area indices; Agric.For. Meteorol. 51, 35-49.
Warrilow, D.A., A.B. Sangster and A. Slingo (1986): Modelling of land surface processes and their influence on European climate; UK Met.Office, Bracknell, England, 92 pp.
Webb, E.K., G.I. Pearman and R. Leuning (1980): Correction of flux measurements for density effects due to heat and water vapour transfer; Q.J.R.Meteorol.Soc. 106, 85-100.
Wieringa, J. (1993): Representative roughness parameters for homogeneous terrain; Boundary-Layer Meteorol. 63, 323-363.
Wilson, N.R. and R.H. Shaw (1977): A higher-order closure model for canopy flow; J.Appl.Meteorol. 16,1198-1205.
Wilson, J.D., B.J. Legg and D.J. Thomson (1983): Correct calculation of particle trajectories in the presence of a gradient in turbulent velocity variance; Boundary-Layer Meteorol. 27,163-169.
Winkel, T. and S. Rambai (1990): Stomatal conductance of some grapevines growing in the field under a Mediterranean environment; Agric.For.Meteorol. 51,107-121.
Wiscombe, W.J. and S.G. Warren (1980): A model for the spectral albedo of snow. 1: Pure snow; ].Atmos.Sci. 37,2712-2733.
Wong, S.C., I.R. Cowan and G.D. Farquhar (1979): Stomatal conductance correlates with photosynthetic capacity; Nature 282, 424-426.
Wyngaard, J.C. (1988): Flow distortion effects on scalar flux measurements in the surface layer: implications for sensor design; Boundary-Layer Meteorol. 42,19-26.
Wyngaard, J.C, Y. Izumi and S.A. Collins Jr. (1971): Behaviour of the refractive-index-structure parameter near the ground; J.Opt.Soc.Am. 61,1646-1650.
Xue, Y., P.J. Sellers, J.L. Kinter and J. Shukla (1991): A simplified biosphere model for global climate studies; J.Climate 4, 345-364.
2 7 0 Sparse canopy parameterizations for meteorological models
Curriculum
Bartholomeus Johannes Josephus Martinus van den Hurk (geboren op 19 november 1963 te Heeze, Noord-Brabant) legde de eerste twee jaar van de middelbare school af op het Strabrecht College in Geldrop. In 1982 behaalde hij het VWO examen aan het vd Putt-lyceum in Eindhoven, en begon aan een studie Milieuhygiëne, oriëntatie Luchthygiëne en -verontreiniging, aan de Landbouwuniversiteit Wageningen. Gedurende zijn studietijd zat hij een jaar in het bestuur van studentenvereniging SSR, en richtte in 1987 samen met zijn broer Stone De Stichting Lens op, een amateur muziektheater-gezelschap. In 1989 studeerde hij af, na een tweetal afstudeervakken Meteorologie, twee afstudeervakken Luchthygiëne, en een stage bij Dennis Baldocchi aan het Atmospheric Turbulence and Diffusion Division van NOAA in Oak Ridge, TN USA.
Hierna heeft hij gedurende anderhalf jaar zijn vervangende dienstplicht vervuld aan de Vakgroep Meteorologie van de Wageningse Landbouwuniversiteit. In die periode werkte hij aan diverse kleine projekten, onder begeleiding van Henk de Bruin. Aansluitend aan die periode werd hij aan dezelfde vakgroep aangesteld als wetenschappelijk assistent bij het in dit proefschrift beschreven EFEDA-projekt. Opnieuw onder supervisie van Henk de Bruin coördineerde hij de bijdrage van de vakgroep Meteorologie aan het veldexperiment in Spanje in 1991, en heeft zich daarna ruim een jaar beziggehouden met dataverwerking, contacten onderhouden met andere participanten aan het EFEDA-projekt, en met modelstudies. In de loop van deze periode kwam een gedeeltelijke NWO promotieplaats vrij. Nadat de oorspronkelijke promotie-opdracht enigszins werd aangepast aan de ervaring die hij binnen de EFEDA-werkzaamheden had opgedaan, werd in het kader van de resterende, door NWO gesubsidieerde, aanstelling naar de in dit proefschrift beschreven promotie toegewerkt. Vanaf september 1995 werkt hij via een tijdelijke aanstelling bij het KNMI aan de toepassing van satellietgegevens voor bodemvochtinitialisatie in weermodellen.
Bart van den Hurk is getrouwd met Christien Alferink, en heeft (nog) geen kinderen.
Curriculum 271